Question

The circles on the focal radii of a parabola as diameter touch: A) the tangent at the vertex B) the axis C) the directrix D) latus rectum

Answer 1

`C:(x-a)(a-at^2)+(y-0)(y-2at)=0`
`x^2-ax-at^2x+a^2t^2+y^2-2aty=0-(1)`
tangent to vertex, x=0-(2)
`y^2-2aty+a^2t^2=0`
`(y-at)^2=0`
`y=at,at`
Circle touches line x=0.
for axis, y=0
`x^2-x(a+at^2)+a^2t^2=0`
not a perfect square.
option a is correct.