M0IITU09 - Circles & system of circles qns -...

1
QUEST TUTORIALS
Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. If the line x + 2 by + 7 = 0, is a diameter
of the circle, x
2
+ y
2
- 6x + 2y = 0
then b =
(A) 3 (B) - 5
(C) - 1 (D) 5
2. The equation of the circle which
touches both the axes & whose radius
is a, is :
3. The centres of the circles, x
2
+ y
2
= 1,
x
2
+ y
2
+ 6x - 2y = 1 & x
2
+ y
2
- 12x + 4y =
1 are :
4. If a circle passes through the point
(0, 0), (a, 0), (0, b), then its centre is
5. The line l x + my + n = 0 will be a
tangent to the circle, x
2
+ y
2
= a
2
if :
(A) n
2
( l
2
+ m
2
) = a
2
(B) a
2
( l
2
+ m
2
) = n
2
(C) n ( l + m) = a (D) a ( l + m) = n
6. The angle between the two tangents
from the origin to the circle,
(x - 7)
2
+ (y + 1)
2
= 25 is :
(A) 0 (B)
π
3
(C)
π
6
(D)
π
2
7. The locus of the middle points of
those chords of the circle, x
2
+ y
2
= 4
which subtend a right angle at the
origin is :
8. A pair of tangents are drawn from the
origin to the circle, x
2
+ y
2
+ 20 (x + y)
+ 20 = 0 . The equation of the pair of
tangents is :
9. y = mx is a chord of a circle of radius
a and the diameter of the circle lies
along x-axis and one end of the chord
is origin . The equation of the circle
described on this chord as diameter is
:
10. If two circles, (x - 1)
2
+ (y - 3)
2
= r
2
and
x
2
+ y
2
- 8x + 2y + 8 = 0 intersect in
two distinct points, then :
(A) 2 < r < 8 (B) r = 2
(C) r < 2 (D) r > 2
11. The equation of the circle which
touches both axes & whose centre is
(x
1
, y
1
) is :
2 = 0
2
= 0
2 + y
1
2
Circles & System of Circles

2
QUEST TUTORIALS
Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
12. The lines, 2x - 3y = 5 & 3x - 4y = 7
are the diameters of a circle of area
154 sq. units . The equation of the
circle is :
13. A circle touches the y-axis at the point
(0, 4) & cuts the x-axis in a chord of
length 6 units . The radius of the circle
is :
14. If the line l x + my = 1 be a tangent to
the circle x
2
+ y
2
= a
2
, then the locus
of the point ( l , m) is :
(A) A straight line (B) A circle
(C) A parabola (D) None of these