If a tangent to the parabola $y^{2} = a x$ makes an angle 45° with x-axis, its point of contact will be

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$(- a / 2, a / 4)$

$(- a / 4, a / 2)$

$(a / 2, a / 4)$

$(a / 4, a / 2)$

answer is C.

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Detailed Solution

$\begin{array}{l} m = \tan 45^{\circ} = 1, 4 A = a ⇒ A = a / 4 \\ p o i n t o f c o n t a c t = (\frac{A}{m^{2}}, \frac{2 A}{m}) \\ = (\frac{a}{4}, \frac{a}{2}) \end{array}$

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