Show that the line $x - y + 4 = 0$ is a tangent to the parabola $y^{2} = 16 x$ . Find the point of contact.

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Solution

$\begin{matrix} \Rightarrow x - y = 4 \Rightarrow y = x - 4 \Rightarrow x = 1 a n d y^{2} = 16 x ∴ a = 4 \Rightarrow T h e n, p o i n t o f c o n t a c t i s (\frac{a}{m^{2}}, \frac{2 a}{m}) (\frac{a}{m^{2}}, \frac{2 a}{m}) = (\frac{4}{{(1)}^{2}}, \frac{2 \times 4}{1}), (4, 8) A n s . \end{matrix}$

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