Question

Find the equation of the curve at every point of which the tangent line has a slope of 2x:

Options

• `x = - y^2 + c`

• `y = -x^2 + c`

• `y = x^2 + c`

• `x = y^2 + c`

Answer 1

`y = x^2 + c`

Explanation:

Slope of tangent line ⇒ `(dy)/(dx) = 2x`

∴ `dy = 2x  dx`

Integrating both the sides, we get

`int dy = int 2x  dx`

`y = 2 xx x^2/2 + c`

∴ `y = x^2 + c`.

This is the required equation of curve.