The locus of the mid-point of the chord of   contact of tangents drawn from points lying on the straight line

4x  5y = 20 to the circle x 2 + y 2 = 9 is

(A)  20(x 2 + y 2 )  36x + 45y = 0  (B)  20(x 2 + y 2 ) + 36x  45y = 0

(C)  36(x 2 + y 2 )  20x + 45y = 0  (D)  36(x 2 + y 2 ) + 20x  45y = 0

let the point on the line 4x-5y=20 be A.

let the coordinates of the point A is given by

then the equation of the chord of contact from point A to the circle is given by;

let the locus of the mid-point of the chord of contact be P(h,k).

therefore the equation of the chord with mid-point (h,k) is given by;

equation (1) and (2) represent the same straight line,

therefore

......(3)

now substitute the value of a,

since P(h,k) is a variable point. therefore replace h by x and k by y.

the required locus is 

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