# How do you find the equation of the tangent and normal line to the curve #y=x^2# at x=-3?

##### 1 Answer

Aug 26, 2016

Equation of the tangent

#y=-6x-9#

Equation of the Normal

#y=1/6x+19/2#

#### Explanation:

Given -

#y=x^2#

It is a quadratic function. The curve is a upward facing parabola.

Its first derivative gives the slope at any given point on the curve.

#dy/dx=2x#

Slope exactly at

#m_1=2(-3)=-6#

At

The tangent and Normal are passing through the point

Slope of the tangent is

Steps to get Equation of the tangent -

#mx+c=y#

#(-6)(-3)+c=9#

#18+c=9#

#c=9-18=-9#

Equation of the tangent is -

#y=-6x-9#

Steps to get Equation of the Normal -

Normal's slope

#mx+c=y#

#1/6(-3)+c=9#

#-1/2+c=9#

#c=9+1/2=(18+1)/2=19/2#

Equation of the Normal -

#y=1/6x+19/2#