From a point A(t) on the parabola `y^(2)=4ax`, a focal chord and a tangent are drawn. Two circles are drawn in which one circle is drawn taking focal chord AB as diameter and other is drawn by taking the intercept of tangent between point A and point of the circles is

Options

A. the line joining focus and p
B. the line joining focus and A
C. tangent to the parabola at point A
D. none of these

Answer

C

Explanation

(3) Circle `S_(2)`, taking focal chord AB as diameter will touch directrix at point P and circle `S_(1)` taking AP as diameter will pass through focus S (since AP subtends angle `90^(@)` at focal of parabola).

Hence, the common chord of the given circles is line AP (which is the intercept of tangent at point A between point A and directrix).