Question

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

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