# How do you find the equations for the normal line to #x^2/32+y^2/8=1# through (4,2)?

##### 2 Answers

The normal line to the curve through the point

#### Explanation:

For a curve in implicit form:

the normal line to the point

We have:

so that the line normal to the curve in

or multypling everything by 4 to have integral coefficients:

#### Explanation:

The tangent at

This works for any conic section anywhere, with suitable further substitution rules. More complex rules give chords.