Question

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

Solution

Correct option is

 

The equation of the chords of contact of tangents from (x1y1) and (x2,y2) to the given hyperbola are  

           

  

Lines (i) and (ii) are at right angles. 

.

SIMILAR QUESTIONS

Q1

Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c2.

Q2

 

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.

Q3

 

The vertices of the hyperbola

     

Q4

 

The centre of the hyperbola

       

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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