Question

Let  be two points on the hyperbola . If (hk) is the point of intersection of the normal of P and Q, then k is equal to

Solution

Correct option is

 

The coordinates (hk) of the point of intersection of the normals at P andQ are given by   

       

  

We have, 

         

      

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

If the line y = 2x + λ be a tangent to the hyperbola 36x2 – 25y2 = 3600, then λ is equal to     

Q8

From any point on the hyperbola  tangents are drawn to the hyperbola . The area cut-off by the chord of contact on the asymptotes is equal to

Q9

PQ and RS are two perpendicular chords of the rectangular hyperbola xyc2. If C is the centre of the rectangular hyperbola, then the product of the slopes of CPCQCR and CS equal to  

Q10

If x = 9 is the chord of contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is