CircleHard

Question

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line4x - 5y = 20 to the circle x2 + y2 = 9 is

Options

A.20(x2 + y2 ) - 36x + 45y = 0
B.20(x2 + y2 )+ 36x - 45y = 0
C.36(x2 + y2 )- 20x + 45y = 0
D.36(x2 + y2 )+ 20x - 45y = 0

Solution


            
Equation of the chord bisected at P (h, k)
hx + ky = h2 + k2  ......(i)
Let any point on line be
Equation of the chord of contact is
⇒ ax +        ......(ii)
Comparing (i) and (ii)

Now,
20 (h2 + k2) = 9 (4h - 5k)
20 (x2 + y2) - 36x + 45y = 0.

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