Question

Tangent are drawn from any point on the hyperbola  to the circle x2 + y2 = 9. If the locus of the mid-point of the chord of contact is

  

Solution

Correct option is

7873

Equation of the chord of contact of a point  on the hyperbola is with respect to the circle is

                  … (1)

Let M(h, k) be the mid-point of (1), then equation of (1) in terms of the mid-point is

      hx + ky = h2 + k2

Since (1) and (2) represent the same line.

      

 Locus of (h, k) is

    

or  4(x2 + y2)2 = 36x2 – 81y2

which is same as a(x2 + y2)2 = bx2 – cy2

 = 4, b = 36, c = 81

     a2 + b2 + c2 = 16 + 1296 + 6561 = 7873.

SIMILAR QUESTIONS

Q1

Find the locus of the mid-points of the chord of the parabola y2 = 4ax which subtend a right angle at the vertex.

Q2

If the parabola C and D intersect at a point A on the line L1, then equation of the tangent point L at A to the parabola D is

Q3

If a > 0, the angle subtended by the chord AB at the vertex of the parabola is

Q4

P is a point on the circle C, the perpendicular PQ to the major axis of the ellipse E meets the ellipse at M, then  is equal to

Q5

Equation of the diameter of the ellipse conjugate to the diameter respected by L is 

Q6

 

If R is the point of intersection of the line L with the line x = 1, then 

Q7

If L is the chord of contact of the hyperbola H, then the equation of the corresponding pair of tangents is

Q8

If R is the point of intersection of the tangents to H at the extremities  of the chord L, then equation of the chord contact of with respect to the parabola P is

Q9

If the chord of contact of R with respect to the parabola Pmeets the parabola at T and T’, S is the focus of the parabola, then Area of the triangle STT’ is equal to

Q10

If l is the length of the intercept made by a common tangent to the circle x2 + y= 16 and the ellipse , on the coordinate axes, then 81l2+ 3 is equal to