Coordinate Geometry is one of the most scoring and conceptually rich topics in the JEE Mathematics syllabus. Mastering JEE Coordinate Geometry requires a strong foundation in concepts, regular practice, and problem-solving skills. In this article, we’ll see a step-by-step guide to help you master Coordinate Geometry for JEE Mains and Adanced.

### JEE Mains Coordinate Geometry Syllabus

The Coordinate Geometry syllabus for JEE Mains includes the following chapters and topics:

- Straight Lines
- Circles
- Parabolas
- Ellipses
- Hyperbolas

Each of these topics requires a deep understanding of concepts and the ability to solve a variety of problems.

## How to Master JEE Coordinate Geometry

### 1. Understand the Basics

**Coordinate System:**Start with understanding the Cartesian plane, the x-axis, y-axis, and the concept of coordinates.**Distance Formula:**Learn and practice using the distance formula to find the distance between two points.**Section Formula:**Understand how to divide a line segment in a given ratio using the section formula.**Slope of a Line:**Grasp the concept of the slope and how it determines the steepness and direction of a line.**Equation of a Line:**Familiarize yourself with different forms of equations of a line (slope-intercept, point-slope, and two-point form).

### 2. Master Key Concepts

**Straight Lines:**Study various forms of the equation of a line, the angle between two lines, the condition for perpendicularity and parallelism, and the concept of image of a point in a line.**Circles:**Understand the standard equation of a circle, the radius, diameter, and tangents to a circle. Also, learn the concepts of chord, secant, and the power of a point.**Parabola, Ellipse, and Hyperbola:**Get familiar with the standard forms of these conic sections, their directrices, foci, and eccentricities. Understand their properties and how to derive equations based on given conditions.

### 3. Practice Regularly

**Solve Problems:**Start with basic problems to apply concepts and gradually move to complex JEE-level problems.**Use JEE Question Banks:**Solve problems from previous years’ JEE papers and various question banks focusing on Coordinate Geometry.**Time Management:**Practice solving problems under timed conditions to improve speed and accuracy.

### 4. Work on Visualization

**Graphical Representation:**Always try to visualize the problem by sketching graphs. This helps in better understanding and solving problems related to lines, circles, and conics.**Visualize with Graphs:**Regularly draw graphs by hand to better understand geometric transformations and relations. This hands-on practice will enhance your ability to visualize problems and verify solutions, which is essential for mastering Coordinate Geometry.

### 5. Memorize Important Formulas

**Formula Sheet:**Create a formula sheet with all important equations, theorems, and results related to Coordinate Geometry. Regular revision will help in quick recall during exams.

### 6. Focus on Application-Based Problems

**Locus Problems:**Work on problems that involve finding the locus of a point under given conditions. These problems often appear in JEE.**Intersection of Figures:**Practice problems where you need to find the intersection of two geometric figures, such as lines and circles, or circles and conics.

### 7. Analyze and Learn

**Review Mistakes:**After solving problems, review your solutions and understand any mistakes you made. Analyze different methods to solve the same problem.**Join Study Groups:**Discuss complex problems with peers or join online study groups to get different perspectives on problem-solving.

### 8. Regular Revision

**Weekly Revision:**Dedicate time each week to revise key concepts and formulas. This ensures that you retain the information.**Mock Tests:**Take regular mock tests to assess your understanding and identify areas that need more focus.

In conclusion, to master JEE Coordinate Geometry, it’s important to understand the basics, solve different types of questions, and learn to visualize problems with graphs. Stay disciplined, practice regularly, and approach each problem with confidence, and you’ll be well on your way to achieving a high score in JEE Coordinate Geometry.

## JEE Coordinate Geometry Questions (PYQ)

Here are some multiple-choice questions (MCQs) on Coordinate Geometry that have been asked in previous years’ JEE exams:

**Question 1:**

The equation of the circle passing through the origin and making intercepts *a* and *b* on the coordinate axes is:

- (a)
*x*^{2}+ y^{2}= ax + by - (b)
*x*^{2}+ y^{2}= a^{2}+ b^{2} - (c)
*x*^{2}+ y^{2}– ax – by = 0 - (d)
*x*^{2}+ y^{2}= ax + by + ab

**Answer:** (c) *x ^{2} + y^{2} – ax – by = 0*

**Question 2:**

The locus of the mid-point of the chord of the circle *x ^{2} + y^{2} = r^{2}* which subtends a right angle at the origin is:

- (a) A circle with radius
*r/√2* - (b) A circle with radius
*r* - (c) A circle with radius
*r/2* - (d) A straight line

**Answer:** (a) A circle with radius *r/√2*

**Question 3:**

If a line *y = mx + c* is a tangent to the parabola *y ^{2} = 4ax*, then the value of

*c*is:

- (a)
*-a/m* - (b)
*a/m* - (c)
*a/m*^{2} - (d)
*2a/m*

**Answer:** (b) *a/m*

**Question 4:**

The point *(2, 3)* is rotated counterclockwise about the origin through an angle of *90°*. The new coordinates of the point are:

- (a)
*(-3, 2)* - (b)
*(3, -2)* - (c)
*(2, -3)* - (d)
*(-2, 3)*

**Answer:** (a) *(-3, 2)*

**Question 5:**

The equation of the pair of straight lines passing through the origin and perpendicular to the pair of lines given by *2x ^{2} + 6xy + 3y^{2} = 0* is:

- (a)
*2x*^{2}+ 6xy + 3y^{2}= 0 - (b)
*6x*^{2}– 7xy + 3y^{2}= 0 - (c)
*2x*^{2}– 6xy + 3y^{2}= 0 - (d)
*2x*^{2}– 6xy – 3y^{2}= 0

**Answer:** (c) *2x ^{2} – 6xy + 3y^{2} = 0*

**Question 6:**

If the distance between the foci of a hyperbola is 10 units and the distance between its directrices is 12 units, then the eccentricity of the hyperbola is:

- (a)
*5/6* - (b)
*6/5* - (c)
*5/4* - (d)
*4/3*

**Answer:** (b) *6/5*

**Question 7:**

The locus of the point of intersection of perpendicular tangents to the parabola *y ^{2} = 4ax* is:

- (a)
*x + y = a* - (b)
*x*^{2}= 2ay - (c)
*x + y = 2a* - (d)
*x*^{2}= 4ay

**Answer:** (d) *x ^{2} = 4ay*

**Practice more with the below resources : **

JEE Mains Previous Year Questions

JEE Advanced Previous Year Questions