Coordinate Geometry is one of the key topics in the CAT Quantitative Ability (QA) section. Usually, the sums in Coordinate Geometry are not tough to solve and hence one must not miss out on the questions on Coordinate Geometry. You can check out these Coordinate Geometry questions from the CAT Previous year’s papers. Practice a good number of questions in CAT Coordinate Geometry so that you can answer these questions with ease in the exam. In this post, we will look into some important Coordinate Geometry Questions for CAT QA. These are a good source for practice; If you want to practice these questions, you can download this Important CAT Coordinate Geometry Questions PDF below, which is completely Free.
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Question 1: What is the equation of a circle with centre of origin and radius is 6 cm?
a)
b)
c)
d)
1) Answer (C)
Solution:
Given,
Center of the circle = (0,0)
Radius of the circle (r) = 6 cm
Hence, the correct answer is Option C
Question 2: The equation of circle with centre (1, -2) and radius 4 cm is:
a)
b)
c)
d)
2) Answer (D)
Solution:
Given,
Centre of the circle (a, b) = (1, -2)
Radius of the circle (r) = 4 cm
Hence, the correct answer is Option D
Question 3: In
a) 9 cm
b) 10 cm
c) 7.5 cm
d) 12.5 cm
3) Answer (B)
Solution:
Given D is midpoint of AC so,
AD =
But also given AC = AB
AD =
AD is a tangent and APB is a secant. So the tangent secant theorem can be applied,
AB = 10 cm
Question 4: The graph of the equations
a) 4
b) 6
c) -4
d) -3
4) Answer (A)
Solution:
15x – 6y + 3 = 0 —(1)
15x – 20y – 25 = 0 —(2)
From eq (1) and (2),
14y + 28 = 0
y = -2
From eq(1),
15x + 6
x = -1
=
Question 5: What is the area (in square units) of the triangular region enclosed by the graphs of the equations x + y = 3, 2x + 5y = 12 and the x-axis?
a) 2
b) 3
c) 4
d) 6
5) Answer (B)
Solution:

x + y = 3
2x + 2y = 6 —(1)
2x + 5y = 12 —(2)
From eq (1) and eq (2),
3y = 6
y = 2
So height = 2
y = 0 —(3)
put the value of y in eq(1) and (2),
2x = 6
x = 3
And 2x = 12
x = 6
Area =
=
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Question 6: The graphs of the equations
a) 13
b) -11
c) 15
d) -9
6) Answer (C)
Solution:
From eq (1) and (2),
7y = 35
y = 5 =
From eq (1),
2x = -4
x = -2 =
Now,
The graph of the equations
So,
x = -12 =
= -2 + 12 + 5 + 0 = 15
Question 7: The point of intersection of the graphs of the equations 3x — 5y = 19 and 3y —7x + 1 =0 is P
a) -2
b) -1
c) 1
d) 0
7) Answer (B)
Solution:
The point of intersection of the graphs of the equations 3x — 5y = 19 and 3y —7x + 1 =0 is P
So,
3
7
Eq(1) multiply by 3 and eq (2) multiply by 5,
9
35
From eq (3) and (4),
26
From eq (1),
3
Now,
=
= -1
Question 8: The graph of the equation x — 7y = —42, intersects the y-axis at
a)
b) 6
c)
d) 5
8) Answer (A)
Solution:
The graph of the equation x — 7y = —42, intersects the y-axis at
So, x = 0
0 – 7y = -42
y = 6
graph of 6x + y – 15 = 0, intersects the x-axis at
So, y = 0
6x – 15 = 0
x = 5/2
Now,
= 0 + 6 + 5/2 + 0 =
Question 9: The graphs of the equations
a) 4
b) -4
c) 3
d) 5
9) Answer (D)
Solution:
When graphs of the equations intersect at the point
On eq(1) + (2),
From the eq(2),
Now,
Question 10: The graph of x + 2y = 3 and 3x – 2y = 1 meet the Y-axis at two points having distance
a)
b)
c) 1 units
d) 2 units
10) Answer (D)
Solution:
on Y axis, x=0
put x = 0 in x+2y = 3
2y = 3
putting x=0 in 3x-2y = 1
-2y = 1
therefore points on Y-axis are
required distance =
Question 11: ABCDis a cyclic quadrilateral, AB and DC when produced meet at P, if PA = 8 cm, PB = 6 cm, PC = 4 cm, then the length (in cm) of PDis
a) 6
b) 12
c) 8
d) 10
11) Answer (B)
Solution:

Given that,PA = 8 cm, PB = 6 cm, PC = 4 cm
As per tangent & secant rule,
=>
Question 12: In a circle, chords AD and BC meet at a point E outside the circle. If
a)
b)
c)
d)
12) Answer (C)
Solution:

In cyclic quadrilateral ABCD, sum of opposite angles = 180
From the figure,
In
Hence, the correct answer is Option C
Question 13: If
a)
b)
c)
d)
13) Answer (B)
Solution:

Let
In
In
In
Hence, the correct answer is Option B
Question 14: In
a)
b)
c)
d)
14) Answer (B)
Solution:

Given,
In
OB is the angular bisector of
Let
OC is the angular bisector of
Let
From the figure,
In
In
Hence, the correct answer is Option B
Question 15: The distance between the centres of two circles of radius 2.5 cm each is 13 cm. The length (in cm)of a transverse common tangent is:
a) 12
b) 8
c) 6
d) 10
15) Answer (A)
Solution:
Radius of first circle (
Radius of second circle (
The distance between centres of two circles (
Hence, the correct answer is Option A
Question 16: ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and
a)
b)
c)
d)
16) Answer (D)
Solution:

In cyclic quadrilateral ABCD, sum of opposite angles = 180
Angle subtended by diameter in a semicircle is 90
In
Hence, the correct answer is Option D
Question 17: In
a)
b)
c)
d)
17) Answer (A)
Solution:

Given,
In
OB is the angular bisector of
Let
OC is the angular bisector of
Let
From the figure,
In
In
Hence, the correct answer is Option A
Question 18: PA and PB are the tangents to a circle with centre O, from a point P outside the circle. A and B are the points on the circle. If
a)
b)
c)
d)
18) Answer (C)
Solution:

Given,
PA and PB are the tangents to the circle with centre O
In quadrilateral OAPB,
In
Angles opposite to equal sides are equal in triangle
In
Hence, the correct answer is Option C
Question 19: The distance between the centres of two circles of radius 3 cm and 2 cm is 13 cm. The length (in cm) of a transverse common tangent is:
a) 8
b) 12
c) 6
d) 10
19) Answer (B)
Solution:
Radius of first circle (
Radius of second circle (
The distance between centres of two circles (
Hence, the correct answer is Option B
Question 20: The distance between the centre of two circles of radius 4 cm and 2 cm is 10 cm. The length (in cm) of a transverse common tangent is:
a) 4
b) 6
c) 10
d) 8
20) Answer (D)
Solution:
Given, distance between centres of circles
Radius of first circle
Radius of second circle
=
Question 21: Chords AB and CD of a circle intersect externally at P. If AB = 6 cm, CD = 3 cm and PB = 4 cm, then the length (in cm) of PD is:
a) 5
b) 7
c) 6
d) 2
21) Answer (A)
Solution:

Given,
AB = 6 cm, CD = 3 cm and PB = 4 cm
Let PD =
If chords AB and CD of a circle intersect externally at P then
Hence, the correct answer is Option A
Question 22: There are two circles of radius 5 cm and 3 cm respectively. The distance between their centres is 10 cm. The length (in cm) of a transverse common tangent is:
a) 9
b) 8
c) 10
d) 6
22) Answer (D)
Solution:
Given, distance between centres of circles
Radius of first circle
Radius of second circle
Question 23: The chord of the contact of tangents drawn from point on the circle
a) 5
b) 4
c) 6
d) 2
23) Answer (B)
Solution:
The chord of the contact of tangents drawn from point on the circle
Given,
Comparing equation (1) and equation (2)
p = 2, m = 1, n = 1
Hence, the correct answer is Option B
Question 24: O is the centre of a circle to which PAX and PBY are tangents from point P at points A and B.Q is a point on the circle, such that
a)
b)
c)
d)
24) Answer (D)
Solution:
.jpg)
Given,
PAX and PBY are tangents at A and B respectively to the circle
Angles opposite to equal sides in a triangle are equal
OA = OQ
OB = OQ
Hence, the correct answer is Option D
Question 25: In
a)
b)
c)
d)
25) Answer (D)
Solution:
_PlEc8It.jpg)
BD
In
In
Hence, the correct answer is Option D