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JEE Questions for Maths Circle And System Of Circles Quiz 14 - MCQExams.com
JEE
Maths
Circle And System Of Circles
Quiz 14
The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation x
2
+ 2x – 3 = 0 and the abscissae are the roots of the equation y
2
+ 4y −12 = 0 is
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x2 + y2 + 2x + 4y – 15 = 0
0%
x2 + y2 – 4x – 2y – 15 = 0
0%
x2 + y2 + 4x + 2y – 15 = 0
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none of these
If p and q be the longest distance and the shortest distance respectively of the point (–7,from any point (α, β) on the curve whose equation is x
2
+ y
2
– 10x – 14y – 51 = 0, then G.M. of p and q is equal to
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0%
0%
2)
0%
13
0%
none of these
The equation of the circumcircle of an equilateral triangle is x
2
+ y
2
+ 2gx + 2fy + c = 0 and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is
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4(x2 + y= g2 + f2
0%
4(x2 + y+ 8gx + 8fy = (1 – g)(1 + 3g) + (1 – f)(1 + 3f)
0%
4(x2 + y+ 8gx + 8fy = g2 + f2
0%
none of these
A line meets the co-ordinate axes an A and B. A circle is circumscribed about the ∆ ABO. If p and q are the distances of the tangents to the circle at the origin from the points A and B respectively, then the diameter of the circle is
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0%
q (p + q)
0%
p + q
0%
p (p + q)
0%
p (p – q)
C
1
is a circle of radius 1 touching the x – axis and the y-axis. C
2
is another circle of radius > 1 and touching the axes as well as the circle C
1
. Then the radius of C
2
is
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0%
0%
2)
0%
0%
none of these
A region in the xy-plane is bounded by the curve x
2
+ y
2
= 25 and the line y = 0. If the point (p, p +lies in the in term of the region, then
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p ∈ (–1, 3)
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p ∈ (– ∞, –∪ (3, ∞)
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p ∈ (– 4, 3)
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p ∈ (– ∞, – 1)
Let f(x, y) = 0 be the equation of a circle. If f (0, λ) = 0 has equal roots λ = 2, 2 and f (λ,= 0 has roots λ = 4/5, 5, then the centre of the circle is
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0%
0%
2)
0%
0%
none of these
If (2,is a point interior to the circle x
2
+ y
2
– 6x – 10y + λ = 0 and the circle does not cut the axes at any point, then λ belongs to the interval
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0%
(25, 32)
0%
(9, 32)
0%
(32, + ∞)
0%
none of these
A foot of the normal from the point (4,to a circle is (2,and a diameter of the circle has the equation 2x – y = 2. Then the equation of the circle is
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0%
x2 + y2 + 2x – 1 = 0
0%
x2 + y2 – 2x – 1 = 0
0%
x2 + y2 – 2y – 1 = 0
0%
none of these
The equation of the smallest circle passing through the intersection of the line x + y =1 and the circle x
2
+ y
2
= 9 is
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0%
x2 + y2 + x + y – 8 = 0
0%
x2 + y2 – x – y – 8 = 0
0%
x2 + y2 – x + y – 8 = 0
0%
none of these
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