How do you find the equations for the normal line to #x^2+y^2=9# through (0,3)?
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.
The line segment joining
Differentiate using the chain rule to get
The vertical line through