1
QUEST
TUTORIALS
Head Office
: E16/289, Sector8, 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 :
x
2
2
 2
ax  2
ay + a
2
= 0
x
2
2
+ ax + ay = 0
x
2
2
+ 2
ax + 2
by  a
2
None of these
3.
The centres of the circles, x
2
2
= 1,
x
2
+
y
2
+
6x

2y
=
1
& x
2
+
y
2

12x
+
4y
=
1 are :
Same
Collinear
(C) Non

collinear
(D) None of these
4.
If a circle passes through the point
(0, 0), (a, 0), (0, b), then its centre is
(a, b)
(b, a)
a
b
2
2
,
b
a
2
2
,

5.
The line
l
x
+
my
+
n = 0 will be a
tangent to the circle,
x
2
2
= a
2
if :
n
2
(
l
2
+ m
2
) = a
2
a
2
(
l
2
2
) = n
2
n
(
l
+ m) = a
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 :
0
π
3
π
6
π
2
7.
The locus of the middle points of
those chords of the circle,
x
2
2
= 4
which subtend a right angle at the
origin is :
x
2
+ y
2
 2x  2y = 0
x
2
2
x
2
2
= 2
(x  1)
2
+ (y  2)
2
= 5
8.
A pair of tangents are drawn from the
origin to the circle, x
2
2
+ 20 (x + y)
+ 20 = 0 . The equation of the pair of
tangents is :
x
2
2
+ 10
xy = 0
x
2
2
+ 5
2
x
2
y
2
2
x
2
y
2
 5
9.
y = mx is a chord of a circle of radius
a and the diameter of the circle lies
along xaxis and one end of the chord
is origin . The equation of the circle
described on this chord as diameter is
:
(1 + m
2
) ( (x
2
2
)  2
ax = 0
(1
2
) (x
2
+ y
2
)

2a
(x
+ my) = 0
+
m
2
2
+
y
2
) + 2a
(x
+
my) = 0
(D) (1
+
m
2
2
+
y
2
)

2a
(x

10.
If two circles, (x

1)
2
+ (y

3)
2
= r
2
and
x
2
2
 8x + 2y + 8 = 0 intersect in
two distinct points, then :
2 < r < 8
r = 2
r < 2
r > 2
11.
touches both axes & whose centre is
(x
1
, y
1
) is :
x
2
2
+ 2x
1
(x
+
y)
+ x
1
2
x
2
2

2x
1
(x
+
y) + x
1
2
x
2
+ y
2
= x
1
2
1
2
x
2
2
xx
1
yy
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Circles & System of Circles