The locus of the midpoints of the focal chords of the parabola y2=4ax is

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The locus of the midpoints of the focal chords of the parabola $y^{2} = 4 ax$ is

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$y^{2} = a (2 x - a)$

$y^{2} = 2 a (x + a)$

$y^{2} = 2 a (x - a)$

$y^{2} = a (2 x + a)$

answer is B.

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Detailed Solution

$Given parabola y^{2} = 4 ax Let A = ({at}^{2}, 2 at), B = (\frac{a}{t^{2}}, \frac{- 2 a}{t}) be end points focal chord Let P (x, y) be l o c u s o f m i d p o i n t o f f o c a l c h o r d AB t h e n 2 x = {at}^{2} + \frac{a}{t^{2}}, 2 y = 2 at - \frac{2 a}{t} 2 x = a [{(t - \frac{1}{t})}^{2} + 2] y = a (t - \frac{1}{t}) 2 x = a [\frac{y^{2}}{a^{2}} + 2] y^{2} = 2 a (x - a)$ Question Image