13 Coordinate Geometry PYQ (Solutions)

Master Coordinate Geometry for CAT 2026 with practice questions and detailed explanations

CAT 2025

Coordinate Geometry (analytical geometry involving lines, circles, and curve equations) has been almost entirely absent from recent CAT QA papers. From 2017 to 2024, CAT has shown a strong preference for pure Euclidean geometry—triangles, quadrilaterals, circles, and basic mensuration—rather than coordinate-based equation problems.

CAT 2017–2019: No significant coordinate geometry questions; geometry was purely classical.
CAT 2020: Slot-1’s “Functions, Graphs and Statistics” category may have included 1 simple graph-based question, but it was not a traditional coordinate geometry problem.
CAT 2021–2024: Continued the trend of 0 direct coordinate geometry questions across slots.

Expected Weightage:
Coordinate geometry is effectively absent in CAT QA for 2017–2024, with 0 direct questions in nearly all years. CAT consistently prioritizes classical geometry over analytical/coordinate-based questions.

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Weightage Over Past Years

Year	Q.NONumber of questions	Difficulty Level
2024	1	Medium
2023	2	Hard
2022	2	Medium
2020	3	Medium
2019	2	Hard
2017	3	Medium

CAT 2024 Coordinate Geometry questions

Question 1

Slot-3

For some constant real numbers $p, k$ and $a$ , consider the following system of linear equations in $x$ and $y$ :
$px - 4y = 2$
$3x + ky = a$
A necessary condition for the system to have no solution for $(x, y)$ is

$2a+k\neq0$

$ap-6=0$

$ap+6=0$

$kp+12\neq0$

CAT 2023 Coordinate Geometry questions

Question 1

Slot-1

Let $\mathrm{C}$ be the circle $x^2+y^2+4x-6y-3=0$ and $\mathrm{L}$ be the locus of the point of intersection of a pair of tangents to $\mathrm{C}$ with the angle between the two tangents equal to $60^{\circ}$ . Then, the point at which $L$ touches the line $x=6$ is

(6,4)

(6,8)

(6,3)

(6,6)

Question 2

Slot-2

The area of the quadrilateral bounded by the Y -axis, the line x=5 , and the lines |x−y|−|x−5|=2 , is

CAT 2022 Coordinate Geometry questions

Question 1

Slot-1

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (-2, 8), respectively. Then, the coordinates of the vertex D are

(-4, 5)

(4, 5)

(-3, 4)

(0, 11)

Question 2

Slot-3

In a triangle $\mathrm{ABC}, \mathrm{AB}=\mathrm{AC}=8 \mathrm{cm}$ . A circle drawn with $\mathrm{BC}$ as diameter passes through $\mathrm{A}$ . Another circle drawn with center at A passes through B and $\mathrm{C}$ . Then the area, in sq. $\mathrm{cm}$ , of the overlapping region between the two circles is

$16(\pi-1)$

$32(\pi-1)$

$32 \pi$

$16 \pi$

CAT 2020 Coordinate Geometry questions

Question 1

Slot-3

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

$\frac{14π}{3}$

$\frac{123π}{7}$

$\frac{205π}{9}$

$\frac{12π}{5}$

Question 2

Slot-3

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

Question 3

Slot-3

The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

CAT 2019 Coordinate Geometry questions

Question 1

Slot-1

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

Question 2

Slot-2

Let a, b, x, y be real numbers such that a² + b² = 25 , x² + y² = 169 and ax + by = 65. If k = ay - bx, then

k = 0

k > $\frac{5}{13}$

k = $\frac{5}{13}$

0 < k ≤ $\frac{5}{13}$

CAT 2017 Coordinate Geometry questions

Question 1

Slot-1

The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

4π

2π

Question 2

Slot-1

The shortest distance of the point $\left(\tfrac{1}{2}, 1\right)$ from the curve $y = |x - 1| + |x + 1|$ is

$\sqrt{2}$

$\sqrt{32 \frac{3}{2}}$

Question 3

Slot-2

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

$ -5 $

$ -6 $

$ -7 $

$ -8 $

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13 Coordinate Geometry PYQ (Solutions)

Weightage Over Past Years

For some constant real numbers p,kp, kp,k and aaa, consider the following system of linear equations in xxx and yyy: px−4y=2px - 4y = 2px−4y=2 3x+ky=a3x + ky = a3x+ky=a A necessary condition for the system to have no solution for (x,y)(x, y)(x,y) is

The area of the quadrilateral bounded by the Y -axis, the line x=5 , and the lines |x−y|−|x−5|=2 , is

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (-2, 8), respectively. Then, the coordinates of the vertex D are

The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

The area, in sq. units, enclosed by the lines x = 2, y = |x - 2| + 4, the X-axis and the Y-axis is equal to

The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

Let a, b, x, y be real numbers such that a² + b² = 25 , x² + y² = 169 and ax + by = 65. If k = ay - bx, then

The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is

The shortest distance of the point (12,1)\left(\tfrac{1}{2}, 1\right)(21​,1) from the curve y=∣x−1∣+∣x+1∣y = |x - 1| + |x + 1|y=∣x−1∣+∣x+1∣ is

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

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For some constant real numbers $p, k$ and $a$ , consider the following system of linear equations in $x$ and $y$ :
$px - 4y = 2$
$3x + ky = a$
A necessary condition for the system to have no solution for $(x, y)$ is

The shortest distance of the point $\left(\tfrac{1}{2}, 1\right)$ from the curve $y = |x - 1| + |x + 1|$ is