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Circle described on the focal chord as diameter touches the tangent at the vertexA. the axisB. the tangent at the vertexC. the directrixD. none of these |
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Answer» Correct Answer - B 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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