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

Explanation

`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

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