﻿ The locus of a point P(α, β) moving under the condition that the line y = αx + β is a tangent to the hyperbola  : Kaysons Education

# The Locus Of A Point P(α, β) Moving Under The Condition That The Line y = αx + β Is A Tangent To The Hyperbola

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## Question

### Solution

Correct option is

A hyperbola

If y = αx + β touches the hyperbola , then

which represents a hyperbola.

#### SIMILAR QUESTIONS

Q1

Find the equation of the hyperbola whose asymptotes are x + 2y + 3 = 0 and 3x + 4y + 5 = 0 and which passes through the point

(1,–1 ). Find also the equation of the conjugate of the conjugate hyperbola.

Q2

The vertices of the hyperbola

Q3

The centre of the hyperbola

Q4

The eccentricity of the hyperbola with latusrectum 12 and semi-conjugate axis , is

Q5

The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latusrectum 4, is given by

Q6

The equation of the tangent to the curve 4x2 – 9y2 = 1 which is parallel to 4y = 5x + 7, is

Q7

The equation of the tangent parallel to y = x drawn to  is

Q8

If m is a variable, the locus of the point of intersection of the lines  is a/an

Q9

If the chords of contact of tangents from two points (x1y1) and (x2y2) to the hyperbola  are at right angles, then  is equal to

Q10

The equation of the chord joining two points (x1y1) and (x2y2) on the rectangular hyperbola xy = c2 is