# The circles on focal radii of a parabola as diameter touch

Q: The circles on focal radii of a parabola as diameter touch

(A) the tangent at the vertex

(B) the axis

(C) the directrix

(D) none of these

Sol: Any point on parabola y2 = 4ax with focus S (a, 0) is P(at2 , 2at).

Centre of circle with PS as diameter is C $\large (\frac{a(1+t^2)}{2} , a t )$ and radius $\large = \frac{a}{2}(1+t^2)$

clearly the distance of centre C from tangent at vertex is equal to radius.

Hence (A) is the correct answer.