Home
Class 11
MATHS
A circle of radius r intersects a rectan...

A circle of radius r intersects a rectangular hyperbola whose centre is at C, at four points P,Q,R and S. If `CP^(2)+ CQ^(2)+ CR^(2)+ CS^(2)=ar^(2)`, then the value of'a' be -

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE|10 Videos

  • DIAGRAMMATIC REPRESENTATION OF DATA

    CHHAYA PUBLICATION|Exercise EXERCISE (Very short Answer Type Question)|7 Videos

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

Similar Questions

Explore conceptually related problems

If the circle x^2+y^2=a^2 intersects the hyperbola x y=c^2 at four points P(x_1, y_1),Q(x_2, y_2),R(x_3, y_3), and S(x_4, y_4), then

Let C be a curve which is the locus of the point of intersection of lines x=2+m and m y=4-mdot A circle s: (x-2)^2+(y+1)^2=25 intersects the curve C at four points: P ,Q ,R ,a n dS . If O is center of the curve C , then O P^2+O Q^2+O R^2+O S^2 is (a) 50 (b) 100 (c) 25 (d) (25)/2

Suppose the circle having equation x^2+y^2=3 intersects the rectangular hyperbola x y=1 at points A ,B ,C ,a n dDdot The equation x^2+y^2-3+lambda(x y-1)=0,lambda in R , represents.

If the circle C_(2) of radius 5 intersects othe circle C_(1):x^(2)+y^(2)=16 such that the common chord is in maximum length and its slope is (3)/(4) , then the centre of C_(2) will be-

In the adjoining figure, two tangents drawn from external point C to a circle with centre O touches the circel at the point P and Q respectively. A tangent drawn at another point R of the circle intersects CP and CQ at the points A and B respectively. If CP = 7 cm and BC =11 cm, then determine the length of BR.

AB is a diameter of a circle with centre O , P is any point on the circle, the tangent drawn through the point P intersects the two tangents drawn through the points A and B at the points Q and R respectively. If the radius of the circle be r , then prove that PQ.PR=r^(2) .

Prove that the points P(-1,-2) Q (7,4) R (4,8) and S(-4,2) are the vertices of a rectangle.

In a rectangular hyperbola x^2-y^2=a^2 , prove that SP.S'P=CP^2 , where C is the centre and S, S' are the foci and P is any point on the hyperbola.

If S, S' are the foci and' P any point on the rectangular hyperbola x^2 - y^2 =a^2 , prove that, bar(SP).bar(S'P) = CP^2 where C is the centre of the hyperbola