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If $2 y = 5 x + k$ is a tangent to the parabola $y^{2} = 6 x$ then $k =$

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$\frac{3}{5}$

$\frac{2}{3}$

$\frac{4}{5}$

$\frac{6}{5}$

answer is D.

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Detailed Solution

$y^{2} = 6 x \Rightarrow$ $H e r e = 4 a = 6 \Rightarrow a = \frac{3}{2}$

$2 y = 5 x + k$

$y = \frac{5 x}{2} + \frac{k}{2}$

$m = \frac{5}{2}, c = \frac{k}{2}$

$∴ c = \frac{a}{m} \Rightarrow \frac{k}{2} = \frac{3 / 2}{5 / 2} \Rightarrow \frac{k}{2} = \frac{3}{5}$

$∴ k = \frac{6}{5}$

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