JEE Questions for Maths Circle And System Of Circles Quiz 14 - MCQExams.com

The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation x2 + 2x – 3 = 0 and the abscissae are the roots of the equation y2 + 4y −12 = 0 is
  • x2 + y2 + 2x + 4y – 15 = 0
  • x2 + y2 – 4x – 2y – 15 = 0
  • x2 + y2 + 4x + 2y – 15 = 0
  • 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 x2 + y2 – 10x – 14y – 51 = 0, then G.M. of p and q is equal to

  • Maths-Circle and System of Circles-14447.png
  • 2)
    Maths-Circle and System of Circles-14448.png
  • 13
  • none of these
The equation of the circumcircle of an equilateral triangle is x2 + y2 + 2gx + 2fy + c = 0 and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is
  • 4(x2 + y= g2 + f2
  • 4(x2 + y+ 8gx + 8fy = (1 – g)(1 + 3g) + (1 – f)(1 + 3f)
  • 4(x2 + y+ 8gx + 8fy = g2 + f2
  • 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
  • q (p + q)
  • p + q
  • p (p + q)
  • p (p – q)
C1 is a circle of radius 1 touching the x – axis and the y-axis. C2 is another circle of radius > 1 and touching the axes as well as the circle C1. Then the radius of C2 is

  • Maths-Circle and System of Circles-14452.png
  • 2)
    Maths-Circle and System of Circles-14453.png

  • Maths-Circle and System of Circles-14454.png
  • none of these
A region in the xy-plane is bounded by the curve x2 + y2 = 25 and the line y = 0. If the point (p, p +lies in the in term of the region, then
  • p ∈ (–1, 3)
  • p ∈ (– ∞, –∪ (3, ∞)
  • p ∈ (– 4, 3)
  • 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

  • Maths-Circle and System of Circles-14457.png
  • 2)
    Maths-Circle and System of Circles-14458.png

  • Maths-Circle and System of Circles-14459.png
  • none of these
If (2,is a point interior to the circle x2 + y2 – 6x – 10y + λ = 0 and the circle does not cut the axes at any point, then λ belongs to the interval
  • (25, 32)
  • (9, 32)
  • (32, + ∞)
  • 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
  • x2 + y2 + 2x – 1 = 0
  • x2 + y2 – 2x – 1 = 0
  • x2 + y2 – 2y – 1 = 0
  • none of these
The equation of the smallest circle passing through the intersection of the line x + y =1 and the circle x2 + y2 = 9 is
  • x2 + y2 + x + y – 8 = 0
  • x2 + y2 – x – y – 8 = 0
  • x2 + y2 – x + y – 8 = 0
  • none of these
0:0:1


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