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
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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

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- Spring '11
- Friesner
- Algebra, New Delhi, pH., x2 + y2
-
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