The locus of mid points of chords of the parabola $y^{2} = 4 a x$ passing through the foot of the directrix on axis is

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

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

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

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

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Solution

The correct option is B $y^{2} = 2 a (x + a)$
Let $(h, k)$ be the mid point of the chord.
Then equation of chord is given by $k y - 2 a (x + h) = k^{2} - 4 a h$
$(- a, 0)$ will satisfies the equation.
$- 2 a (- a + h) = k^{2} - 4 a h$
$\Rightarrow y^{2} = 2 a (x + a)$ is the required locus.
Hence, option 'B' is correct.

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Similar questions

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

y^{2} = 4 a x

y^{2} = 2 a x

A (t_{1})

B (t_{2})

C (t_{3})

y^{2} = 4 a x,

A B

y^{2} = 4 a x

y^{2} = 4 a x

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