Comprehensive Mathematics Chapter: Circles MCQs

Name ................................................

Batch.................... Roll No. ...............
JEE MAIN ONLINE EXAM - MATHEMATICS
18-02-2023
23P/TP/C Circles Batch: LT-24 Special (G-1-5)


In part I (20 Questions). Each question has four options (1),(2), (3) & (4). Only one of these four
option is correct. Each correct answer will be awarded four mark. One mark will be deducted for
each incorrect answer.
1. If one end of a diameter of the circle 2x2 + 2y2 - 4x - 8y + 2 = 0 is ( 3 , 2 ) , the other end is ;
1) ( 2 , 3 ) 2) ( 4 , -2 ) 3) ( 2 , -1 ) 4) ( -1 , 2 )
2. Two circles of equal radius r cut orthogonally. If their centres are (2, 3) and (5, 6) then r =
1) 1 2) 2 3) 3 4) 4
3. The circle whose equation is x2 + y2 - 2ax - ay + a2 = 0 :
1) passes through origin 2) touches only x axis 3) touches only y axis 4) touches both the axis
4. The radius of the circle passing through the point (6, 2), two of whose diameters are x + y = 6 and
x + 2y = 4 is:
1) 10 2) 2 5 3) 6 4) 4

5. The two circles x 2  y2  ax and x 2  y 2  c2  c  0  touch each other if

1) a  c 2) a  2c 3) a  2c 4) 2 a  c

6. The locus of the point  , m  . So that x  my  1 touches the circle x 2  y2  a 2 , is

1
2) x  y 
2 2
1) x 2  y2  ax  0
a2

3) y2  4ax 4) x 2  y 2  ax  ay  a 2  0

7. The value of  so that the line 3x  4y   touches x 2  y 2  4x  8y  5  0 are
1) 35,15 2) 3, –5 3) 35, 15 4) 3,5

8. The circles x 2  y2  6x  2y  8  0 and x 2  y 2  2x  6y  1  0
1) touch internally 2) touch externally
3) interesect each other 4) do not intersect
9. Find the equation of the circle whose centre is (3, 4) and which touches the line 5x + 12y = 1

381
1) x2 + y2 – 6x – 8y + =0 2) x2 + y2 – 6x + 7y + 381 = 0
169

381
3) x2 + y2 – 8x + 7y + =0 4) x2 + y2 – 7x + 8y – 381 = 0
169
10. The equation of a circle of radius r and touching both the axis is
1) x 2  y2  2rx  0 2) x 2  y2  2ry  0

3) x 2  y 2  2rx  2ry  c  0 4) x 2  y 2  2rx  2ry  r 2  0

, 23P/TP/P 2 J - MATHEMATICS

11. The equation of the circle whose diameters are 2x - 3y + 12 = 0 and x + 4y - 5 = 0 and area 154 square
units is

1)  x  32   y  2 2  49 2)  x  32   y  2 2  49

3)  x  3 2   y  3 2  25 4)  x  3 2   y  32  25
12. A circle passes through (0, 0), (a, 0) and (0, b). The co-ordinate of its centre are:
1) (b/2, a/2) 2) (a/2, b/2)
3) (a, b) 4) (b, a)
13. The equation of the circle which passes through the origin and cuts off intercepts 3 and 4 from the positive
parts of the axes respectively
2 2 2 2
 3 5  3 5
 x     y  2     x     y  2   
2 2
1) 2)
 2  2  2  2

2 2 2 2
 2 5  2 5
3)  x     y  2     4)  x     y  2    
2 2

 3  4    3  3  

14. The circles x2 + y2 + 2ax + c = 0 and x2 + y2 + 2by + c = 0 touch if:

1 1 1 1 1 1
1)   2) 2
 2 
a b c a b c

1 1 1 1 1 1
3) 2
 2  2 4)  
a b c a 2 b2 c
15. The equation of the chord of the circle x2 + y2 - 6x + 8y = 0 bisected at the point (5, -3) is :
1) x + y = 7 2) 2x + y = 7
3) x - y = 7 4) 2x - y = 7
16. The centre of the circle passing through (0,0) and (1,0) and touching the circle x2+y2=9 is

1 1 1 
1)  ,  2)  ,  2 
2 2 2 

3 1  1 3
3)  ,  4)  , 
2 2
   2 2
17. A circle is given by x2 + y2 + 4x - 7y + 12 = 0. The points are such that P(0, 0) and Q(-2, 4) are such that
1) both lie inside the circle
2) both lie outside the circle
3) one lies inside and other lies outside the circle
4) one lies on the circle and other lies inside the circle
18. A circle of radius 5 units touches the co ordinate axes in the first quadrant. If the circle makes a complete
roll on X axis along the +ve direction of X axis then its equation in new position is

1)  x   5  3     y  52  52 2)  x   5  8     y  5 2  52
2 2




3)  x   5  8    y  32  52
2
4)  x   5  10     y  5   5 2
2 2