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The locus of the centriod of triangle formed by a tangent to $y^{2} = 36 x$ with co-ordinate axes is

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$y^{2} = - 3 x$

$y^{2} = 3 x$

$y^{2} = 9 x$

$y^{2} = - 9 x$

answer is B.

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Detailed Solution

$y^{2} = 36 x \Rightarrow a = 9, O (0, 0) A (- 9 t^{2} 0)$

$B (0, 9 t); G (x, y) = (- 3 t^{2}, - 3 t)$

$Elimination ' t' \Rightarrow y^{2} = - 3 x$

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