Updated On : February 12, 2024
Reader's Digest: Want to know the ins and outs of CBSE Class 11 Applied Maths Coordinate Geometry 2024? Read this blog to learn the concept, project topics, syllabus, weightage & prep tips!
Exciting news for CBSE students! The board has announced 'Applied Maths' as a fresh subject addition. Now, you might wonder, "What's the big deal?"
Even though you might have studied Coordinate Geometry in your regular Maths lessons, the approach in Applied Maths takes a whole new turn.
Diving into the syllabus, Coordinate Geometry consists of three sub-topics. First, we have the "Straight Lines," which forms the foundational pillar.
Next is the "Conic Sections," which focuses on circles and parabolas, offering a fascinating perspective on curves. And lastly, for those with a knack for visualizing beyond the 2D realm, there's an "Introduction to Three-Dimensional Geometry."
Here's a quick fact: out of the entire CBSE Class 11 Applied Maths blueprint, Coordinate Geometry hold a weightage of 5 marks, neatly spread across 15 periods.
CBSE recommends the ever-reliable NCERT as your go-to guide for Applied Maths Coordinate Geometry to aid you in this mathematical journey.
This blog aims to provide you with invaluable insights into this subject, covering key aspects such as:
Coordinate Geometry, often called analytic geometry or Cartesian geometry, is a branch of mathematics that employs algebraic equations to represent and analyze geometric figures on a coordinate plane.
In this, geometric figures such as points, lines, and curves are represented using coordinates and algebraic equations.
The coordinate system is typically the Cartesian coordinate system, which utilizes two perpendicular lines called axes (the x-axis representing the horizontal direction and the y-axis representing the vertical direction) to define a point uniquely in a plane using a pair of numerical coordinates.
To better understand the concept of coordinate geometry, consider the simple example of a point in a plane.
In the Cartesian coordinate system, a point is an ordered pair of numbers represented P (x,y), where x is the distance of the point from the y-axis (called the x-coordinate or abscissa), and y is the distance from the x-axis (called the y-coordinate or ordinate).
For instance, the point P (3,2) represents a point 3 units to the right of the y-axis and 2 units above the x-axis. This systematic approach allows for a seamless blend of algebra and geometry, facilitating the study of figures and spaces' shapes, sizes, and properties using algebraic methods.
Read More - CBSE Class 11 Commerce Subjects List 2024
This subject is designed to develop significant mathematical skills and methods needed in other subject areas. Topics covered in two years aim to enable students to use mathematical knowledge in business, economics and social sciences.
Read More: CBSE Class 11 Applied Maths - Mathematical Reasoning
In class 11 coordinate geometry, you will study only three topics: Straight Lines, Conic sections (Circles and parabolas), and Introduction to Three - Dimensional Geometry. The coordinate geometry holds a weightage of 13 marks in the CBSE class 11 Applied Maths subject.
The table below shows the CBSE class 11 Applied Maths Coordinate Geometry Syllabus:
Topics | Learning Outcomes | Explanation of Topics |
---|---|---|
Straight Lines | Find the slope and equation of a line in various form Find the angle between the two lines Find the perpendicular from a given point on a line Find the distance between two parallel lines |
Gradient of a line Equation of line: Parallel to axes, point-slope form, two-points form, slope intercept form, intercept form Application of the straight line in the demand curve related to economic problems |
Conic Sections | Define a circle Find different forms of equations of a circle Solve problems based on applications of circle |
Circle as a locus of a point in a plane Equation of a circle in standard form, central form, diameter form and general form |
Introduction to Three-Dimensional Geometry | Define parabola and related terms Define eccentricity of a parabola Derive the equation of a parabola |
A parabola as a locus of a point in a plane. Equation of a parabola in standard form: Focus, Directrix, Axis, Latus rectum, Eccentricity Application in a parabolic reflector, beam supported by wires at the end of the support, girder of a railway bridge, etc. |
Read More: CBSE Class 11 Applied Math Books
Here are some project topic ideas for CBSE Class 11 Applied Maths Coordinate Geometry:
Check Out - CBSE Class 11 Commerce Books
From the syllabus for CBSE Class 11 Applied Maths Coordinate Geometry 2024, here are the most important topics:
Straight Lines:
Conic Sections:
Introduction to Three-Dimensional Geometry:
Check Also: CBSE Class 11 Applied Maths Probability
A structured and comprehensive approach is vital to tackle CBSE Class 11 Applied Maths Coordinate Geometry effectively. Here's a strategy based on the provided syllabus:
Understand the Basics
Straight Lines
Conic Sections
Introduction to Three-Dimensional Geometry
Practice Regularly
Conceptual Clarity Over Rote Learning
Maintain a Formula Sheet
Analyze Errors
Visualize Problems
Find More: Differences between Pure Maths and Applied Maths
To help you understand the type of questions asked in the exam, we have provided some sample questions for your reference here.
Q1) How are the points (0, 1), (3, 1) and (1, 3) situated with respect to the circle x 2 + y 2 – 2x – 4y + 3 = 0?
Answer: To check the position of a point to a circle, substitute the point in the circle equation.
For (0,1): 02+12−0−4(1)+3=002+12−0−4(1)+3=0 So, the point lies on the circle.
For (3,1) and (1,3), substituting them in the equation, we get values greater than 0. So, they lie outside the circle.
Q2) Obtain the equation of the circle orthogonal to both the circles x 2 + y 2 + 3x – 5y + 6 = 0 and 4x 2 + 4y 2 – 28x + 29 = 0 and whose centre lies on the line 3x + 4y + 1 = 0.
Answer: The given problem requires detailed calculation using the properties of orthogonal circles and the conditions they satisfy.
Q3) The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to the circle x 2 + y 2 = 1 pass through a fixed point.
Answer: Using the T = 0 condition, the chord of contact for the tangents from any point (h, k) to the given circle is ℎ+xy=1hx+ky=1
Q1) Find the equation of the straight line, which makes an angle of 15° with the positive direction of the x-axis and cuts an intercept of length 4 on the negative direction of the y-axis.
Solution:
Given that the line makes an angle of 15° with the positive direction of the x-axis, we have tan(θ)=tan(15°)tan(θ)=tan(15°). The slope m of the line is the value of tan(θ).
Now, m=tan(15°)
Using the value of tan(15°)=2−3tan(15°)=2−√ 3 (you can use trigonometric identities or a calculator), m=2−√ 3
The line cuts an intercept of length 4 on the negative direction of the y-axis, so the y-intercept c=-4.
Using the slope-intercept form y=mx+c, y=(2−√ 4)x−4. That is the required equation of the line.
Check Also: CBSE Class 11 Numerical Application
In conclusion, introducing Applied Maths as a subject in CBSE Class 11 brings a fresh perspective to Coordinate Geometry. This blog highlights the essential aspects of this subject, including its syllabus, weightage, benefits, and key concepts.
Here are the key takeaways:
Check Also: CBSE Class 11 Applied Maths Algebra
Frequently Asked Questions
Should I take applied maths in class 11?
Which Mathematics subject is harder? The pure one or the applied one?
What are the topics students will study in CBSE class 11 Applied mathematics coordinate geometry?
What is the weightage of coordinate geometry topic?
What is the importance of studying CBSE Class 11 Applied Maths Coordinate Geometry?
What topics are covered in the CBSE Class 11 Applied Maths Coordinate Geometry syllabus for 2024?
How much weightage does Coordinate Geometry hold in CBSE Class 11 Applied Maths 2024?
What is the recommended resource for studying CBSE Class 11 Applied Maths Coordinate Geometry?
Can you explain the concept of Coordinate Geometry in CBSE Class 11 Applied Maths briefly?
February 12, 2024
Reader's Digest: Want to know the ins and outs of CBSE Class 11 Applied Maths Coordinate Geometry 2024? Read this blog to learn the concept, project topics, syllabus, weightage & prep tips!
Exciting news for CBSE students! The board has announced 'Applied Maths' as a fresh subject addition. Now, you might wonder, "What's the big deal?"
Even though you might have studied Coordinate Geometry in your regular Maths lessons, the approach in Applied Maths takes a whole new turn.
Diving into the syllabus, Coordinate Geometry consists of three sub-topics. First, we have the "Straight Lines," which forms the foundational pillar.
Next is the "Conic Sections," which focuses on circles and parabolas, offering a fascinating perspective on curves. And lastly, for those with a knack for visualizing beyond the 2D realm, there's an "Introduction to Three-Dimensional Geometry."
Here's a quick fact: out of the entire CBSE Class 11 Applied Maths blueprint, Coordinate Geometry hold a weightage of 5 marks, neatly spread across 15 periods.
CBSE recommends the ever-reliable NCERT as your go-to guide for Applied Maths Coordinate Geometry to aid you in this mathematical journey.
This blog aims to provide you with invaluable insights into this subject, covering key aspects such as:
Coordinate Geometry, often called analytic geometry or Cartesian geometry, is a branch of mathematics that employs algebraic equations to represent and analyze geometric figures on a coordinate plane.
In this, geometric figures such as points, lines, and curves are represented using coordinates and algebraic equations.
The coordinate system is typically the Cartesian coordinate system, which utilizes two perpendicular lines called axes (the x-axis representing the horizontal direction and the y-axis representing the vertical direction) to define a point uniquely in a plane using a pair of numerical coordinates.
To better understand the concept of coordinate geometry, consider the simple example of a point in a plane.
In the Cartesian coordinate system, a point is an ordered pair of numbers represented P (x,y), where x is the distance of the point from the y-axis (called the x-coordinate or abscissa), and y is the distance from the x-axis (called the y-coordinate or ordinate).
For instance, the point P (3,2) represents a point 3 units to the right of the y-axis and 2 units above the x-axis. This systematic approach allows for a seamless blend of algebra and geometry, facilitating the study of figures and spaces' shapes, sizes, and properties using algebraic methods.
Read More - CBSE Class 11 Commerce Subjects List 2024
This subject is designed to develop significant mathematical skills and methods needed in other subject areas. Topics covered in two years aim to enable students to use mathematical knowledge in business, economics and social sciences.
Read More: CBSE Class 11 Applied Maths - Mathematical Reasoning
In class 11 coordinate geometry, you will study only three topics: Straight Lines, Conic sections (Circles and parabolas), and Introduction to Three - Dimensional Geometry. The coordinate geometry holds a weightage of 13 marks in the CBSE class 11 Applied Maths subject.
The table below shows the CBSE class 11 Applied Maths Coordinate Geometry Syllabus:
Topics | Learning Outcomes | Explanation of Topics |
---|---|---|
Straight Lines | Find the slope and equation of a line in various form Find the angle between the two lines Find the perpendicular from a given point on a line Find the distance between two parallel lines |
Gradient of a line Equation of line: Parallel to axes, point-slope form, two-points form, slope intercept form, intercept form Application of the straight line in the demand curve related to economic problems |
Conic Sections | Define a circle Find different forms of equations of a circle Solve problems based on applications of circle |
Circle as a locus of a point in a plane Equation of a circle in standard form, central form, diameter form and general form |
Introduction to Three-Dimensional Geometry | Define parabola and related terms Define eccentricity of a parabola Derive the equation of a parabola |
A parabola as a locus of a point in a plane. Equation of a parabola in standard form: Focus, Directrix, Axis, Latus rectum, Eccentricity Application in a parabolic reflector, beam supported by wires at the end of the support, girder of a railway bridge, etc. |
Read More: CBSE Class 11 Applied Math Books
Here are some project topic ideas for CBSE Class 11 Applied Maths Coordinate Geometry:
Check Out - CBSE Class 11 Commerce Books
From the syllabus for CBSE Class 11 Applied Maths Coordinate Geometry 2024, here are the most important topics:
Straight Lines:
Conic Sections:
Introduction to Three-Dimensional Geometry:
Check Also: CBSE Class 11 Applied Maths Probability
A structured and comprehensive approach is vital to tackle CBSE Class 11 Applied Maths Coordinate Geometry effectively. Here's a strategy based on the provided syllabus:
Understand the Basics
Straight Lines
Conic Sections
Introduction to Three-Dimensional Geometry
Practice Regularly
Conceptual Clarity Over Rote Learning
Maintain a Formula Sheet
Analyze Errors
Visualize Problems
Find More: Differences between Pure Maths and Applied Maths
To help you understand the type of questions asked in the exam, we have provided some sample questions for your reference here.
Q1) How are the points (0, 1), (3, 1) and (1, 3) situated with respect to the circle x 2 + y 2 – 2x – 4y + 3 = 0?
Answer: To check the position of a point to a circle, substitute the point in the circle equation.
For (0,1): 02+12−0−4(1)+3=002+12−0−4(1)+3=0 So, the point lies on the circle.
For (3,1) and (1,3), substituting them in the equation, we get values greater than 0. So, they lie outside the circle.
Q2) Obtain the equation of the circle orthogonal to both the circles x 2 + y 2 + 3x – 5y + 6 = 0 and 4x 2 + 4y 2 – 28x + 29 = 0 and whose centre lies on the line 3x + 4y + 1 = 0.
Answer: The given problem requires detailed calculation using the properties of orthogonal circles and the conditions they satisfy.
Q3) The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to the circle x 2 + y 2 = 1 pass through a fixed point.
Answer: Using the T = 0 condition, the chord of contact for the tangents from any point (h, k) to the given circle is ℎ+xy=1hx+ky=1
Q1) Find the equation of the straight line, which makes an angle of 15° with the positive direction of the x-axis and cuts an intercept of length 4 on the negative direction of the y-axis.
Solution:
Given that the line makes an angle of 15° with the positive direction of the x-axis, we have tan(θ)=tan(15°)tan(θ)=tan(15°). The slope m of the line is the value of tan(θ).
Now, m=tan(15°)
Using the value of tan(15°)=2−3tan(15°)=2−√ 3 (you can use trigonometric identities or a calculator), m=2−√ 3
The line cuts an intercept of length 4 on the negative direction of the y-axis, so the y-intercept c=-4.
Using the slope-intercept form y=mx+c, y=(2−√ 4)x−4. That is the required equation of the line.
Check Also: CBSE Class 11 Numerical Application
In conclusion, introducing Applied Maths as a subject in CBSE Class 11 brings a fresh perspective to Coordinate Geometry. This blog highlights the essential aspects of this subject, including its syllabus, weightage, benefits, and key concepts.
Here are the key takeaways:
Check Also: CBSE Class 11 Applied Maths Algebra
Frequently Asked Questions
Should I take applied maths in class 11?
Which Mathematics subject is harder? The pure one or the applied one?
What are the topics students will study in CBSE class 11 Applied mathematics coordinate geometry?
What is the weightage of coordinate geometry topic?
What is the importance of studying CBSE Class 11 Applied Maths Coordinate Geometry?
What topics are covered in the CBSE Class 11 Applied Maths Coordinate Geometry syllabus for 2024?
How much weightage does Coordinate Geometry hold in CBSE Class 11 Applied Maths 2024?
What is the recommended resource for studying CBSE Class 11 Applied Maths Coordinate Geometry?
Can you explain the concept of Coordinate Geometry in CBSE Class 11 Applied Maths briefly?