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  • Mathematics
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Purpose: 1. _Assessment_: To assess the mathematical knowledge and skills of students 2. _Practice_: To provide students with practice questions for improving their mathematical skills 3. _Education_: To educate students on various mathematical concepts and principles

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  • December 6, 2024
  • 11
  • 2024/2025
  • Exam (elaborations)
  • Only questions

Subjects

  • mathematics
  • question paper
  • test
  • exam

Written for

  • Secondary school
  • Mathematics
  • 2
All documents for this subject (2710)

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karishma27704

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CIRCLE 1 PDF(S)
JEE main - Mathematics


Section A
1. The equation of the circle having centre (1, -2) and passing through the point of intersection of lines 3x + y = 14, 2x + 5y
= 18 is

a) x2 + y2 - 2x + 4y - 20 = 0 b) x2 + y2 + 2x + 4y - 20 = 0

c) x2 + y2 + 2x - 4y - 20 = 0 d) x2 + y2 - 2x - 4y - 20 = 0

2. The area of triangle formed by the tangent, normal drawn at (1, √3) to the circle x2 + y2 = 4 and the positive x-axis, is
–



– –
a) 5√3 b) 4√3

– –
c) 2√3 d) √3


3. The equation of the circle of radius 5 and touching the coordinate axes in third quadrant, is
j
a) (x + 4)2 + (y + 4)2 = 25 b) (x + 6)2 + (y + 6)2 = 25
AK

c) (x + 5)2 + (y + 5)2 = 25 d) (x - 5)2 + (y + 5)2 = 25

4. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid-point of the chords of the
circle C that subtend an angle of 2π

3
at its centre is

a) x2 + y2 = 9
b) x2 + y2 = 27

4 4



c) x2 + y2 = 1 d) x2 + y2 = 3

2



5. ax2 + 2y2 + 2bxy + 2x - y + c = 0 represents a circle through the origin, if

a) a = 1, b = 2, c = 0 b) a = 0, b = 0, c = 2

c) a = 2, b = 2, c = 0 d) a = 2, b = 0, c = 0
6. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is

a) (a, b) b) (
b
,−
a
)
2 2




c) (b, a) d) (
a
,
b
)
2 2



7. The equation of a circle whose diameter is the line joining the points (-4, 3) and (12, -1) is

a) x2 + y2 - 8x - 2y - 51 = 0 b) x2 + y2 + 8x - 2y - 51 = 0

c) x2 + y2 + 8x + 2y - 51 = 0 d) x2 + y2 + 8x + 2y + 51 = 0

8. A circle touching the X-axis at (3, 0) and making an intercept of length 8 on the Y-axis passes through the point

a) (2, 3) b) (3, 10)



1/3
***

, c) (1, 5) d) (3, 5)

9. The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the Y-axis and lie in the
first quadrant, is
−−−− − −−−− −
a) x = √1 + 4y , y ≥ 0 b) x = √1 + 2y , y ≥ 0

−−−− − −−−− −
c) y = √1 + 2x , x ≥ 0 d) y = √1 + 4x , x ≥ 0



10. A variable tangent to the circle x2 + y2 = r2 at P cuts the coordinate axes at A and B. The path of midpoint M of AB is
given by

a) 1

x
2
+
1

y
2
= 4r
2
b) r
2
(
1
2
+
1
2
) = 2
x y


2

c) r 2
(
1
+
1
) = 4 d) 1

2
+
1

2
=
r

2
x y
2
x y 4




11. Area of the equilateral triangle inscribed in the circle x2 + y2 - 7x + 9y + 5 = 0 is
– –
a) 175

8
√3 square units b) 185

8
√3 square units
– –
c) square units d) square units
165 155
√3 √3
8 8



12. If the line 2x + 3y = 3 intersects the circle x2 + y2 - 4 = 0 at A and B and M(α, β ) is point of intersection of the tangents
at A and B, then α

β
is equal to:

a) 3

2
b) 2

3



c) 4
d) 3

3 4
j
13. Let L1 be a straight line passing through the origin and L2 be the straight line x + y = 1. If the intercepts made by the
AK

circle x2 + y2 - x + 3y = 0 on L1 and L2 are equal, then which of the following equations can represent L1?

a) x - 7y = 0 b) x - y = 0, x + 7y = 0

c) 7x + y = 0 d) x + y = 0, x - 7y = 0
14. The equation of the circle whose centre is (3, -1) and which cuts off a chord of length 6 on the line 2x - 5y + 18 = 0 is

a) (x + 3)2 + (y + 1)2 = √−−
38
b) (x - 3)2 + (y + 1)2 = √−−
38



c) (x + 3)2 +(y + 1)2 = 38 d) (x - 3)2 +(y + 1)2 = 38

15. If the coordinates of one end of the diameter of the circle x2 + y2 - 8x - 4y + c = 0 are (-3, 2), then the coordinates of
other end are

a) (6, 2) b) (5, 3)

c) (1, -8) d) (11, 2)
16. The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is
of length 3a is

a) x2 + y2 = a2 b) x2 + y2 = 9a2

c) x2 + y2 = 4a2 d) x2 + y2 = 16a2

17. The line lx + my + n = 0 will be a tangent to the circle x2 + y2 = a2 if

a) a2(I2 + m2) = n2 b) n2(l2 + m2) = a2




2/3
***

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