﻿ If a variable line  which is a chord of the hyperbola  subtends a right angle at the centre of the hyperbola then it always touches a fixed circle whose radius is –  : Kaysons Education

If A Variable Line  which Is A Chord Of The Hyperbola  subtends A Right Angle At The Centre Of The Hyperbola Then It Always Touches A Fixed Circle Whose Radius Is –

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Question

Solution

Correct option is

subtends a right angle at centre i.e. (0, 0)

∴ making homogeneous equation of hyperbola

With the help of  and putting coefficient of x2 + coefficient of y2 = 0

‘p’ is also the length of perpendicular drawn from (0, 0) to the line  then radius of circle

SIMILAR QUESTIONS

Q1

If the portion of the asymptotes between center and the tangent at the vertex of hyperbola  in the third quadrant is cut by the line  being parameter, then

Q2

Five points are selected on a circle of radius a. the centers of the rectangular hyperbolas, each passing through four of these pints lie on a circle of a radius

Q3

A, B, C and D are the points of intersection of a circle and a rectangular hyperbola which have different centers. If AB passes through the center of the hyperbola, then CD passes through

Q4

Sa circle with fixed center (3h, 3k) and of variable radius cuts the rectangular hyperbola x2 – y2 = 9a2 at the points A, B, C, D. The locus of the centroid of the triangle ABC is given by

Q5

If PQ is a double ordinate of the hyperbola  such the OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola satisfies –

Q6

A rectangular hyperbola passes through the points A(1, 1), B(1, 5) and C(3, 1). The equation of normal to the hyperbola at A(1, 1) is –

Q7

If values of m for which the line  touches the hyperbola 16x2 – 9y= 144 are the roots of the equation x2 –(a + b)x – 4 = 0, then value of (a + b) is equal to –

Q8

The equation of normal to the rectangular hyperbola xy = 4 at the point P on the hyperbola which is parallel to the line

2x – y = 5 is –

Q9

A tangent to the hyperbola  meets ellipse x2 + 4y2 = 4 in two distinct points. Then the locus of midpoint of this chord is –

Q10

From a point on the line y = x + c, c(parameter), tangents are drawn to the hyperbola  such that chords of contact pass through a fixed point (x1, y1). Then  is equal to –