Question

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

Solution

Correct option is

4ab

 

Let P(x1y1) be a point on the hyperbola

           

The chord of contact of tangents from P to the hyperbola

  is 

         

The equations of the asymptotes are  

       

The points of intersection of (i) with the two asymptotes are given by 

           

         

∴ Area of the triangle 

        

        

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

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