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Coordinate Geometry CAT PYQs , 13 Questions with 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.

Weightage Over Past Years

YearQ.NODifficulty Level
20251Hard
20232Hard
20222Medium
20203Medium
20192Hard
20173Medium

CAT 2025 Coordinate Geometry questions

Question 1

Slot-1

The (x,y)(x, y) coordinates of vertices P,Q\mathrm{P}, \mathrm{Q} and R of a parallelogram PQRS are (−3,−2),(1,−5)(-3,-2),(1,-5) and (9,1)(9,1), respectively. If the diagonal SQ intersects the xx-axis at (a,0)(a, 0), then the value of aa is

$\dfrac{13}{4}$
$\dfrac{29}{9}$
$\dfrac{10}{3}$
$\dfrac{27}{7}$
Show Solution

CAT 2023 Coordinate Geometry questions

Question 1

Slot-1

Let C\mathrm{C} be the circle x2+y2+4x−6y−3=0x^2+y^2+4x-6y-3=0 and L\mathrm{L} be the locus of the point of intersection of a pair of tangents to C\mathrm{C} with the angle between the two tangents equal to 60∘60^{\circ}. Then, the point at which LL touches the line x=6x=6 is

(6,4)
(6,8)
(6,3)
(6,6)
Show Solution

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

Show Solution

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)
Show Solution

Question 2

Slot-3

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

$16(\pi-1)$
$32(\pi-1)$
$32 \pi$
$16 \pi$
Show Solution

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

$\frac{14π}{3}$
$\frac{123π}{7}$
$\frac{205π}{9}$
$\frac{12π}{5}$
Show Solution

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

12
8
6
10
Show Solution

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

15
13
14
12
Show Solution

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

Show Solution

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 ≤ $\frac{5}{13}$
Show Solution

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
4
8
2π
Show Solution

Question 2

Slot-1

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

1
0
$\sqrt{2}$
$\sqrt{32 \frac{3}{2}}$
Show Solution

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 $
Show Solution
Practice all 437 Coordinate Geometry questionsFree, with worked solutions, beyond the previous year papers on this page.

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