Most Common Co-ordinate Geometry Questions for Exams 2025
Co-ordinate Geometry is a high-weightage chapter in JEE Maths, covering straight lines, circles, parabolas, ellipses, and hyperbolas—all crucial for scoring in the exam. This chapter tests your analytical skill, logical reasoning, and ability to visualize geometric loci. Attempt this mock test to reinforce concepts, tackle JEE-level questions, and boost your accuracy under timed exam conditions.
Mock Test Instructions for the Co-ordinate Geometry Mock Test 1:
- 20 questions from Co-ordinate Geometry Mock Test 1
- Time limit: 20 minutes
- Single correct answer per question
- Correct answers appear in bold green after submission
How Can JEE Mock Tests Help You Master Co-ordinate Geometry?
- Identify weak areas in straight lines, circles, parabolas, and conic sections through targeted practice.
- Enhance your speed and accuracy for complex locus and equation-based problems.
- Regular mock tests improve retention of all key co-ordinate geometry formulas.
- Learn the right approach to solve lengthy JEE-level conic and tangency questions under a timer.
- Analyze your mistakes instantly and focus your next revision on uncovered concepts.
Sharpen Your JEE Problem Solving with Expert-Designed Co-ordinate Geometry Mock Tests
- Master the application of section formula, area of triangle, and distance formula in advanced problems.
- Gain confidence by solving JEE previous year-type questions in exam conditions.
- Benefit from detailed solutions and explanations after each question for instant conceptual clarity.
- Get exposure to all varieties of conic section problems—ellipse, hyperbola, and more.
- Strengthen your preparation by continuously benchmarking your scores on chapter-wise tests.
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FAQs on Co-ordinate Geometry Mock Test 2025 – Practice & Solutions
1. What is coordinate geometry?
Coordinate geometry, also called Cartesian geometry, is a branch of mathematics that uses algebraic formulas and numbers to represent and analyze geometric figures by placing them on a coordinate plane. It helps in solving problems related to distances, midpoints, areas, and slopes using coordinates (x, y).
2. What is the distance formula in coordinate geometry?
The distance formula is used to find the length between two points (x₁, y₁) and (x₂, y₂) on a coordinate plane. The formula is:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
This formula is derived from the Pythagorean theorem.
3. How do you find the midpoint of a line segment in coordinate geometry?
The midpoint formula is used to find the exact center point of a line segment joining two points (x₁, y₁) and (x₂, y₂):
Midpoint = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
4. What is the equation of a straight line in the coordinate plane?
The most common equation for a straight line is the slope-intercept form:
y = mx + c
where m is the slope of the line and c is the y-intercept (the value of y when x = 0).
5. How do you find the area of a triangle given its vertices in coordinate geometry?
Given the vertices of a triangle as (x₁, y₁), (x₂, y₂), and (x₃, y₃), the area can be calculated using:
Area = ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|
6. What is the section formula in coordinate geometry?
The section formula finds the coordinates of a point dividing a line segment joining (x₁, y₁) and (x₂, y₂) in the ratio m:n:
P = ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
7. How do you determine if three points are collinear in coordinate geometry?
Three points are collinear if they lie on a single straight line. You can check collinearity by:
- Checking if the area of the triangle formed by the points is zero
- Verifying if the slope between any two pairs of points is the same
8. What is the slope of a line and how is it calculated?
The slope of a line measures its steepness. For points (x₁, y₁) and (x₂, y₂), the slope (m) is:
m = (y₂ - y₁)/(x₂ - x₁)
9. What are the coordinates of the centroid of a triangle?
The centroid of a triangle is the point where its three medians intersect. For vertices (x₁, y₁), (x₂, y₂), (x₃, y₃):
Centroid = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)
10. What is the use of coordinate geometry in real life?
Coordinate geometry is widely used in fields like engineering, navigation, architecture, computer graphics, and GPS technology. It helps in representing and analyzing positions, plotting points, and solving distance-related problems accurately on maps and blueprints.
11. How do you find the equation of a line passing through two given points?
To find the equation of a line passing through points (x₁, y₁) and (x₂, y₂):
1. Calculate the slope (m): m = (y₂ − y₁)/(x₂ − x₁)
2. Use the point-slope form: y − y₁ = m(x − x₁)
12. What is the locus of a point equidistant from two fixed points?
The locus of a point that is equidistant from two fixed points is the perpendicular bisector of the line segment joining those points. This means any point on this line will have equal distance from both given points.
