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Circle described on the focal length as diameter touches the tangent at the vertex

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Circle described on the focal chord as diameter touches the directrix.

Prove that the circle described on the focal chord as a diameter touches the directrix

Knowledge Check

  • The locus of the mid-point of the line segment joining a point on the parabola Y^(2)=4ax and the point of contact of circle drawn on focal distance of the point as diameter with the tangent at the vertex, is

    A
    `y^(2)=9ax`
    B
    `9y^(2)=2ax`
    C
    `2x^(2)=9ay`
    D
    `2y^(2)=9ax`
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