# How do you find the equations for the normal line to #y=x^2# through (2,4)?

##### 1 Answer

Dec 13, 2016

#### Explanation:

The gradient of the tangent to a curve at any particular point is give by the derivative of the curve at that point. The normal is perpendicular to the tangent, so the product of their gradients is

so If

#dy/dx = 2x#

When

and

So the normal we seek passes through

# y-4=-1/4(x-2) #

# :. y-4=-1/4x+1/2#

# :. y=-1/4x+9/2#

We can confirm this graphically: