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Circle described on the focal chord as d...

Circle described on the focal chord as diameter touches

A

the axis

B

the tangent at the vertex

C

the directrix

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let S(a, 0) be the focus of the parabola `y^(2)=4ax`, and `P(at^(2), 2at)` be a point on it. Then equation of a circle on SP as diameter is
`(x-a)(x-at^(2))+(y-0)(y-2at)=0`
It meets y-axis at x = 0
`:." "y^(2)-2"at y"+a^(2)t^(2)=0rArr(y-t)^(2)=0`
This shows that y-axis meets the circle in two coincident points. Hence, the circle touches the tangent at the vertex.
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