Question

Find the equation of tangent and normal to the ellipse $9x^2+16y^2=144$

Answer 1

The equation of tangent to an ellipse is given by $y=mx\pm \sqrt{a^2{m}^2+b^2}$, $m$ being the slope.

Here, $a=4$ and $b=3$, so the equation becomes $y=mx\pm \sqrt{16m^2+9}$

Similarly, the normal equation looks like $y=mx\pm \sqrt{\frac{m(a^2-b^2)}{\sqrt{a^2+b^2{m}^2}}}$

Here, the equation becomes $y=mx\pm \sqrt{\frac{7m}{\sqrt{16+9m}}}$