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Conic Section

The line y ...

Question

The line $y = x + 1$ is a tangent to the curve $y^{2} = 4 x$ at the point.

(1, 2)

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(2, 1)

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(1, 4)

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(2, 2)

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Solution

The correct option is A $(1, 2)$
We have $y = x + 1, y^{2} = 4 x$
Solving these, $\Rightarrow (x + 1)^{2} = 4 x \Rightarrow x^{2} - 2 x + 1 = 0$
$\Rightarrow (x - 1)^{2} = 0 \Rightarrow x = 1 ∴ y = (x + 1)_{x = 1} = 2$
Thus required point of contact is $(1, 2)$

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