### x - VMC Mathematics

```VMC Mathematics
Test: Circles
01. The condition that cx  by  b  0 may touch the circle
2
abc=1
b=ac
greatest
(B) a = c
(D) None of these
distance of the point
(10,7)
from
2
x 2  y 2  16x  55  0
5
(B) 8
(C)
5 5
(D) None of these
 ,   is a point on the circle whose centre is on x-axis
x  y  0 at
and
(2, -2) then the greatest value of
(B) 4  2 2
circle then area of quadrilateral OACB is
2
1
(A)
(B) c g  f
c g2  f 2  c
2
(C) c g  f
2
2
(C) x  2 y  4  0
(D) x  y  1  0
06. If O is the origin and OP and OQ are tangents from the origin to
circle x  y  6 x  4 y  8  0 , the circum centre of
2
OPQis
(B)  3 , 1


(A) (3, -2)
2
(C)  3 ,  1 
4 2 
(D)

3 
,1

 2 
and
intersecting the circle at A and B. Then the area of
(B)
2
(D)
3
a2
7
a
2
(B)  6, 18 


(C)  18 , 6 
5 
(D) None of these

intersection of
5
2
4
(B)
(D)
(B)
x 2  aa  2 y 
2
2
2
2
2
and
is
normal
to
x  y  4 x  2 y  3  0 then (a, b) =
2
(A) (2, 1)
(B) (1, -2)
(C) (1, 2)
(D) (-1, 2)
17. Let A (x`1, y1) B (x2, y2) circles with OA, OB as diameter
drawn. Then the length of the common chord.
(A)
x1 y 2  x 2 y1
2 AB
2 x1 y 2  x 2 y1
AB
(A) x  y  9a
(B)
x1 y 2  x 2 y1
AB
(D) None of these
2
2
(B)
x 2  y 2  16a 2
(C) x  y  4a
(D) x  y  a
19. The equation of the circle having its centre on the line
x  2 y  3  0 and passing through the intersection of
the circle x2 + y2 −2x −-4y + 1 = 0 and
x2 + y2 −4x −-2y + 4 = 0 is
2
2
2

2

(C)
2
2
2
2
2
2
(A) x  y  6 x  7  0
10. The triangle PQR is inscribed in the circle x  y  25 .
If Q & R have coordinates (3, 4) and (-4, 3) respectively
then QPR is
(A)
2
(C) x  y  x  a  (D) x  y   y  a 
15. Two vertices of an equilateral triangle are (-1, 0) and
(1, 0) and third vertex lies above the x-axis. The equation
of its circum circle.
2x
(A) x 2  y 2  2 x  1  0 (B) x 2  y 2 
1 0
3
3
2y
(C) x 2  y 2  2 y  1  0 (D) x 2  y 2 
1 0
3
3
16. The
line
the
circle
ax  by  0 touches
2
2
(A)  6, 18 

5 
c
18. The equation of the circle with origin as centre and
passing through the vertices of an equilateral  whose
median is of length 3a is
2
by x 2  y 2  5 x  3 y  2  0 , the point of
these tangents is



2
2
(C)
09. Tangents are drawn to x  y  12 at points where it is met
2
c
g2  f 2 c
(D)
(A) y  a a  2 x 
AOBis
a2
5
2
14. The locus of the point of intersection of the tangents at
2
x 2  y 2  2ax parallel to the straight line x  2 y  0
a
c
x 2  y 2  2x  4 y  0
07. The circle passing through the distinct points (1, t), (t, 1) and
(t, t) for all values of t passes through the point.
(A) (1, 1)
(B) (-1, -1)
(C)
(1, -1)
(D) (-1, 1)
08. A straight line is drawn through the centre of the circle
(C)
2
2
the point (2, 3) farthest from the centre is
(A) 2 x  3 y  13
(B) 3x  y  3
(A)


touches the circle x  y  2ax  0 is
(D) 4 
2
2
x 2  y 2  2 gx  2 fy  c  0, ' C ' the centre of the
the extremities of a chord of x  y  a which
2
2
05. The equation of the chord of x  y  a passing through
(C)
13. If OA and OB are the tangents from origin to the circle
2
4 2
42 2
(A)
(D) 0

(A)
which touches
 is
(B) 
6
2
(A) 10
(B) 15
(C)
5
(D) None of these
03. The least distance between two points P & Q on the circles
04. If

3

(C)
(A)
x  y  4 x  2 y  20  0 is
2
x  72   y  12  25 is
circle
x 2  y 2  ax  by is
(A)
(C)
02. The
12. The angle between the two tangents from origin to the
2

3

6
11. The number of common tangents that can be drawn to the circle
x2+y24x6y3=0 and x2+y2+2x+2y+1=0 is
(A) 1
(B) 2
(C) 3
(D) 4
VMC, 485 – B, McLeod Road, Rani Ka Bagh, Amritsar.
2
(B) x  y  3 x  4  0
2
2
(C) x  y  2 x  2 y  1  0
2
2
(D) x  y  2 x  4 y  4  0
20. The centre of the circle inscribed in a square formed by the
lines x28x+12=0 and y214y+45=0 is
(A) (4, 7)
(B) (7, 4)
(C) (9, 4)
(D) (4, 9)
21. The length of the tangent from any point on the circle
15x2+15y248x+64y=0 to the two circles
5x2+5y224x+32y+75 =0 and 5x2+5y248x+64y+300=0
are in the ratio of
(A) 1:2
(B) 2:3
(C) 3:4
(D) none of these
2
2
Phone: 9779905879. [email protected]
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Email: [email protected] , Phones: 0183-2291879, 98146-55879
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