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JEE Questions for Maths Circle And System Of Circles Quiz 1 - MCQExams.com
JEE
Maths
Circle And System Of Circles
Quiz 1
The angle between a pair of tangents drawn from a point P to the circle x
2
+ y
2
+ 4x – 6y + 9 sin
2
α + 13 cos
2
α = 0 is 2α. The equation of the locus of the point P is
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0%
x2 + y2 + 4x – 6y + 4 = 0
0%
x2 + y2 + 4x – 6y – 9 = 0
0%
x2 + y2 + 4x – 6y – 4 = 0
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x2 + y2 + 4x – 6y + 9 = 0
Two circles x
2
+ y
2
= 6 and x
2
+ y
2
– 6x + 8 = 0 are given. Then the equation of the circle through their points of intersection and the point (1,is
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0%
x2 + y2 – 6x + 4 = 0
0%
x2 + y2 – 3x + 1 = 0
0%
x2 + y2 – 4y + 2 = 0
0%
none of these
The locus of the mid-point of a chord of the circle x
2
+ y
2
= 4 which subtends a right angle at the origin is
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x + y = 2
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x2 + y2 = 1
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x2 + y2 = 2
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x + y = 1
If a circle passes through the point (a, b) and cuts the circle x
2
+ y
2
= k
2
orthogonally, then the equation of the locus of its centre is
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2ax + 2by - (a2 + b2 + k2 ) = 0
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2ax + 2by - (a2 - b2 + k2 ) = 0
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x2 + y2 - 3ax - 4by + (a2 + b2 - k2 ) = 0
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x2 + y2 - 2ax - 3by + (a2 - b2 - k2 ) = 0
If the 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
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2 < r < 8
0%
r < 2
0%
r = 2
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r > 2
The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is
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0%
x2 + y2 + 2x – 2y = 62
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x2 + y2 + 2x – 2y = 47
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x2 + y2 – 2x + 2y = 47
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x2 + y2 – 2x + 2y = 62
The centre of a circle passing through the points (0, 0), (1,and touching the circle x
2
+ y
2
= 9 is
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0%
0%
2)
0%
0%
The locus of the centre of a circle, which touches externally the circle x
2
+ y
2
– 6x – 6y + 14 = 0 and also touches the y-axis, is given by the equation:
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x2 – 6x – 10y + 14 = 0
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x2 – 10x – 6y + 14 = 0
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y2 – 6x – 10y + 14 = 0
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y2 – 10x – 6y + 14 = 0
The circles x
2
+ y
2
– 10x + 16 = 0 and x
2
+ y
2
= r
2
intersect each other in two distinct points if
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r < 2
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r > 8
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2 < r < 8
0%
If the line y = 7
x
- 25 meets the circle
x
2
+ y
2
= 25 in the points A, B, then the distance between A and B is
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0%
√10
0%
10
0%
5√2
0%
5
The area of the circle centered at (1,and passing through (4,is
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0%
5 π sq units
0%
10 π sq units
0%
25 π sq units
0%
None of these
If two distinct chords, drawn from the point (p, q) on the circle x
2
+ y
2
= px + qy (where pq ≠are bisected by the x –axis, then
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p2 = q2
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p2 = 8q2
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P2 < 8q2
0%
p2 > 8q2
A variable circle passes through the fixed point A (p, q) and touches X - axis. The locus of the other end of the diameter through A is
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(x - p )2 = 4qy
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(x - q )2 = 4py
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(y - p )2 = 4qx
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(y - q )2 = 4px
The equation of two circles which touch the Y - axis at (0,and make an intercept of 8 units on X - axis , are
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x2 + y2 ± 10x - 6y + 9 = 0
0%
x2 + y2 ± 6x - 10y + 9 = 0
0%
x2 + y2 - 8x ± 10y + 9 = 0
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x2 + y2 - 10x ± 6y + 9 = 0
If two diameters of the circles 3
x
2
+ 3y
2
- 6
x
- 18y - 7 = 0 are along the lines 3
x
+ y = c
1
and
x
- 3y = c
2
. Then, the value of c
1
c
2
is
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0%
- 48
0%
80
0%
- 72
0%
54
0%
24
The intercept on the line y =
x
by the circle
x
2
+ y
2
- 2
x
= 0 is AB. Equation of the circle on AB as a diameter, is
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0%
x2 + y2 - x - y = 0
0%
x2 + y2 - x + y = 0
0%
x2 + y2 + x + y = 0
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x2 + y2 + x - y = 0
The equation of the circle of radius 3 that lines in the fourth quadrant and touching the lines
x
= 0 and y = 0, is
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0%
x2 + y2 - 6x + 6y + 9 = 0
0%
x2 + y2 - 6x - 6y + 9 = 0
0%
x2 + y2 + 6x - 6y + 9 = 0
0%
x2 + y2 + 6x + 6y + 9 = 0
The other end of the diameter through the point (-1,on the circle
x
2
+ y
2
- 6
x
+ 4y - 12 = 0 is
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0%
(-7, 5)
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(-7, - 5)
0%
(7, - 5)
0%
(7, 5)
One of the diameter of the circle
x
2
+ y
2
- 12
x
+ 4y + 6 = 0 is given by
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x + y = 0
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x + 3y = 0
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x = y
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3x + 2y = 0
The equation of the circle concentric to the circle 2
x
2
+ 2y
2
- 3
x
+ 6y + 2 = 0 and having area double the area of the circle, is
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0%
8x2 + 8y2 - 24x + 48y - 13 = 0
0%
16x2 + 16y2 + 24x - 48y - 13 = 0
0%
16x2 + 16y2 - 24x + 48y - 13 = 0
0%
8x2 + 8y2 + 24x - 48y - 13 = 0
For a equilateral triangle, the center is the origin and the length af altitude is a. Then, the equation of the circumcircle is
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0%
x2 + y2 = a2
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3x2 + 3y2 = 2a2
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x2 + y2 = 4a2
0%
3x2 + 3y2 = a2
0%
9x2 + 9y2 = 4a2
suppose a circle passes through (2,and (9,and touches the X - axis at P. If O is the origin, then OP is equal to
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0%
4
0%
5
0%
6
0%
9
0%
11
The equation of the circle passing through (4,and having the center (2,is
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0%
x2 + y2 + 4x + 4y - 5 = 0
0%
x2 + y2 - 4x - 4y - 5 = 0
0%
x2 + y2 - 4x = 13
0%
x2 + y2 - 4x - 4y + 5 = 0
The equation of circumcircle of the triangle formed by the lines
x
= 0, y = 0, 2
x
+ 3y = 5, is
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0%
6(x2 + y+ 5 (3x - 2y) = 0
0%
x2 + y2 - 2x - 3y + 5 = 0
0%
x2 + y2 + 2x - 3y - 5 = 0
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6(x2 + y- 5(3x + 2y) = 0
The circle
x
2
+ y
2
- 8
x
+ 4y + 4 = 0 touches
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0%
X - axis
0%
Y - axis
0%
both axes
0%
neither X - axis nor Y - axis
Observe the following statements I . The circle
x
2
+ y
2
- 6
x
- 4y - 7 = 0 touches Y - axis. II. the circles
x
2
+ y
2
+ 6
x
+ 4y - 7 = 0 touches X - axis. Which of the following is correct statement ?
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0%
Both I and II are correct
0%
Neither I nor Ii is correct
0%
I is correct, II is incorrect
0%
I is incorrect, II is correct
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0%
0%
2)
0%
0%
The center of the circle
x
= 2 + 3 cos θ, y = 3 sin θ - 1 is
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0%
(3, 3)
0%
(2, - 1)
0%
(-2, 1)
0%
(1, - 2)
Equation of a circle passing through the origin and making intercept by the line 4
x
+ 3y = 12 with coordinate axes, is
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0%
x2 + y2 + 3x + 4y = 0
0%
x2 + y2 + 3x - 4y = 0
0%
x2 + y2 - 3x + 4y = 0
0%
x2 + y2 - 3x - 4y = 0
The radius of any circle touching the lines 3
x
- 4y + 5 = 0 and 6
x
- 8y - 9 = 0 is
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0%
1.9
0%
0.95
0%
2.9
0%
1.45
The radius of the circle
x
2
+ y
2
+ 4
x
+ 6y + 13 = 0 is
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0%
√26
0%
√13
0%
√23
0%
0
If
x
- y + 1 = 0 meets the circle
x
2
+ y
2
+ y - 1 = 0 at A and b, then the equation of the circle wit AB as diameter, is
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0%
2(x2 + y+ 3x - y + 1 = 0
0%
2(x2 + y+ 3x - y + 2 = 0
0%
2(x2 + y+ 3x - y + 3 = 0
0%
x2 + y2 + 3x - y + 1 = 0
Which of the following equations given circle ?
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0%
r = 2 sin θ
0%
r2 cos 2θ = 1
0%
r( 4 cos θ + 5 sin θ) = 3
0%
5 = r (1 + √2 cos θ)
A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed numbeer (≠ 1). Then, its locus is a
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0%
parabola
0%
circle
0%
hyperbola
0%
pair of straight lines
The circles
x
2
+ y
2
+ 4
x
- 4y + 4 = 0 touches
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0%
X - axis
0%
Y - axis
0%
X - axis and Y - axis
0%
None of these
If a > 2b > 0, then positive value of m for which y = m
x
- b√(1 + m) is a common tangent
x
2
+ y
2
= b
2
and (
x
- a)
2
+ y
2
= b
2
, is
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0%
0%
2)
0%
0%
The equation of the two tangents from (-5, -to the circle
x
2
+ y
2
+ 4
x
+ 6y + 8 = 0 are
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0%
x + 2y + 13 = 0, 2x - y + 6 = 0
0%
2x + y + 13 = 0, x - 2y = 6
0%
3x + 2y + 23 = 0, 2x - 3y + 4 = 0
0%
x - 7y = 23, 6x + 13y = 4
The length (in units) of tangent from point (5,to the circle
x
2
+ y
2
+ 6
x
- 4y - 3 = 0 is
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0%
81
0%
29
0%
7
0%
21
Circle a
x
2
+ ay
2
+ 2g
x
+ 2fy + c = 0 touches X - axis, if
Report Question
0%
f2 > ac
0%
g2 > ac
0%
f2 = bc
0%
g2 = ac
The equation of normal of
x
2
+ y
2
- 2
x
+ 4y - 5 = 0 at (2,is
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0%
y = 3x - 5
0%
2y = 3x - 4
0%
y = 3x + 4
0%
y = x + 1
Locus of the point of intersection of perpendicular tangents to the circle
x
2
+ y
2
= 16 is
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0%
x2 + y2 = 8
0%
x2 + y2 = 32
0%
x2 + y2 = 64
0%
x2 + y2 = 16
If the line y cos α =
x
sin α + a cos α is a tangent to the circle
x
2
+ y
2
= a
2
, then
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sin2 α = 1
0%
cos2 α = 1
0%
sin2 α = a2
0%
cos2 α = a2
The equation of the tangents to the circle
x
2
+ y
2
= 13 at the point whose abscissa is 2, are
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0%
2x + 3y = 13, 2x - 3y = 13
0%
3x + 2y = 13, 2x - 3y =1 3
0%
2x + 3y = 13, 3x - 2y = 13
0%
None of these above
If θ is the angle between the tangents from (-1,to the circle
x
2
+ y
2
- 5
x
+ 4y = 0, then θ is equal to
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0%
2 tan-1 (7/4)
0%
tan-1(7/4)
0%
2 cot-1(7/4)
0%
cot-1(7/4)
length of the tangents from the points (1,to the circles
x
2
+ y
2
+
x
+ y - 4 = 0 and 3
x
2
+ 3y
2
-
x
- y - k = 0 are in the ratio 4 : 3, then k is equal to
Report Question
0%
37/2
0%
4/37
0%
12
0%
7
0%
39/4
If the equation of tangent to the circle
x
2
+ y
2
- 2
x
+ 6y - 6 = 0 and parallel to 3
x
- 4y + 7 = 0 is 3
x
- 4y + k = 0, then the values of k are
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0%
5, -35
0%
-5, 35
0%
7, -32
0%
-7, 32
The locus of the point (l, m), so that l
x
+ my = 1 touches the circles
x
2
+ y
2
= a
2
is
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0%
x2 + y2 - ax = 0
0%
x2 + y2 = 1/a2
0%
y2 = 4ax
0%
x2 + y2 - ax - ay + a2 = 0
0%
x2 - y2 = a2
The equation of tangents drawn from the origin to the circle
x
2
+ y
2
- 2r
x
- 2hy + h
2
= 0 are
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0%
x = 0, y = 0
0%
x = 1, y = 0
0%
(h2 - r2)x - 2rhy = 0, y = 0
0%
(h2 - r2)x - 2rhy = 0, x = 0
The equation of the tangent to the circle
x
2
+ y
2
+ 4
x
- 4y + 4 = 0 which makes equal intercepts on the positive coordinates axes, is
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0%
x + y = 2
0%
x + y = 2√2
0%
x + y = 4
0%
x + y = 8
The length of the tangent drawn to the circle
x
2
+ y
2
- 2
x
+ 4y - 11 = 0 from the point (1,is
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0%
1
0%
2
0%
3
0%
4
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