How do you find the equations for the normal line to #x^2/32+y^2/8=1# through (4,2)?
The normal line to the curve through the point
For a curve in implicit form:
the normal line to the point
so that the line normal to the curve in
or multypling everything by 4 to have integral coefficients:
The tangent at
This works for any conic section anywhere, with suitable further substitution rules. More complex rules give chords.