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Q.

The mirror image of any point on the directrix of the parabola $y^{2} = 4 (x + 1)$ in the line mirror $x + 2 y - 3 = 0$ lies on $3 x - 4 y + 4 k = 0$ then $k =$

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answer is 4.

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Detailed Solution

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Point on directrix is (-2, 0)

$\frac{h - 2}{1} = \frac{K - 0}{2} = \frac{- 2 (- 2 - 3)}{5}$ $(h, k) = (0, 4)$

lies on $3 x - 4 y + 4 k = 0$

$k = 4$

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