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The line y = x + 1 is a tangent to the curve y^2 = 4x at the p

Question

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

(1, 2)

(2, 1)

(1, 4)

(2, 2)

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The line

y = x + 1

is a tangent to the curve

y^{2} = 4 x

at the point.

10 mins ago

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10 mins ago

Text solutionVerified

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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Question Text	The line $y = x + 1$ is a tangent to the curve $y^{2} = 4 x$ at the point.
Answer Type	Text solution:1
Upvotes	150