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: