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The line y = x + 1is a tangent to the c...

The line `y = x + 1`is a tangent to the curve `y^2=4x`at the point(A) `(1, 2)` (B)`(2, 1)` (C) `(1, 2)` (D) `( 1, 2)`

A

`(1, 2)`

B

`(2, 1)`

C

`(1, -2)`

D

`(-1, 2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of curve
`y^(2) = 4x` ….(1)
` rArr 2y(dy)/(dx) = 4 rArr (dy)/(dx) = 2/y`
Slope of tangent at point `(x, y) = 2/y`
Equation of given tangent
` y = x + 1`
Its slope = 1
` :. 2/y = 1 rArr y= 2`
put y = 2 in equation (1)
`2^(2) = 4x rArr x = 1`
` :.` Point of contact = (1, 2)
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