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Question

The circle on focal radii of a parabola as diameter touches the

A
axis
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B
directrix
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C
tangent at vertex
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D
None of these
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Solution

The correct option is B tangent at vertex
Let the parabola be y2=4ax.
Let P(at2,2at) be any point on the parabola.
Then SP is focal radii of the parabola.
The equation of a circle with SP as diameter is
(xa)(xat2)+(y0)(y2at)=0
It meets y-axis at x=0
y22aty+a2t2=0(yat)2=0
y-axis meets the circle only at one point
Therefore, the circle touches the tangent at the vertex.

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