Question

The line is y = x + 1 is a tangent to the curve y² = 4x at the point.

Options

• (1, 2)

• (2, 1)

• (1, –2)

• (–1, 2)

Answer 1

(1, 2)

Explanation:

The Curve is `y^2 = 4x, 2y (dy)/(dx)` = 4

∴ `(dy)/(dx) = 2/(2y) = 2/y`

Slope of the given line, `y = x + 1` is 1.

∴  `2/y` = 1, ∴ `y` = 2 

Putting `y` = 2 in `y^2 = 4x`

`2^2 = 4x`, ∴ `x` = 1 

∴ Point of contact is (1, 2).