﻿ 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 – : Kaysons Education

# 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 –

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## Question

### Solution

Correct option is

2

Let the point be

Chord of contact of hyperbola T = 0

Since this passes through point (x1, y1)

∴  x1 = 2yand y1 c + 1= 0

#### SIMILAR QUESTIONS

Q1

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 –

Q2

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 –

Q3

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 –

Q4

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 –

Q5

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

Q6

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

Q7

Find the eccentricity of the hyperbola whose latus rectum is half of its transverse axis.

Q8

For what value of c does not line y = 2x + c touches the hyperbola 16x2 – 9y2 = 144?

Q9

Determiner the equation of common tangents to the hyperbola  and .

Q10

Find the locus of the mid-pints of the chords of the circle x2 – y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144.