Question

Find the slope of the nomlal to y²=4x at (1,2).

Answer 1

Answer:

$\text{Slope of normal }=-1}$

Step-by-step explanation:

Find the slope of the nomlal to y²=4x at (1,2).

Given curve is

$y^2=4x$

differentiate with respect to x

$2y\:\frac{dy}{dx}=4$

$y\:\frac{dy}{dx}=2$

$\frac{dy}{dx}=\frac{2}{y}$

$\text{Slope of tangent }m=(\frac{dy}{dx})_(1,2)=\frac{2}{2}=1$

$\text{Slope of normal }=\frac{-1}{m}=\frac{-1}{1}=-1$

$\boxed{\text{Slope of normal }=-1}$