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,
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