# How do you find the equations for the normal line to #x^2+y^2=9# through (0,3)?

##### 3 Answers

#### Explanation:

We find the derivative.

We now determine the slope of the tangent.

The normal line is perpendicular to the tangent, so the slope of the normal line will be

Hence, the normal line will be vertical at

Since the point of intersection is

Hopefully this helps!

Here is a solution using geometry.

#### Explanation:

The point

The line segment joining

So the

Here is a solution using calculus, but without implicit differentiation.

#### Explanation:

The point

Differentiate using the chain rule to get

At

The vertical line through