The other extremity of the focal chord of the parabola $y^{2} = 8 x$ which is drawn at the point $(\frac{1}{2}, 2)$ is

(2, - 4)

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(2, 4)

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(8, - 8)

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(8, 8)

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Solution

The correct option is C $(8, - 8)$
Given parabola is $y^{2} = 4 a x$ (where $a = 2)$
we know coordinates of end point of any focal chords are $P (a t^{2}, 2 a t)$ and $Q (a / t^{2}, - 2 a / t)$
Now let $P = (\frac{1}{2}, 2)$ so corresponding $t = \frac{1}{2}$
So other end of the focal chord is $Q (8, - 8)$

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(\frac{1}{2}, 2)

y^{2} = 8 x

(\frac{1}{2}, 2)

y^{2} = 8 x

A focal chord is drawn on the parabola $y^{2} = 8 x$ . if one end of it is (8,8) what is the other end?

y^{2} = 8 x

(\frac{1}{2}, - 2)

(1, 2)

y^{2} = 4 x

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