Mathematics - Ellipse Question with Solution | TestHub

The line is $y=-\frac{\text{ nb }}{\text{ ma }}x-nb$. It will touch the ellipse if $(-nb{)}^2=a^2{\left(-\frac{nb}{ma}\right)}^2+b^2$ $\left[{\mathrm{c}}^2={\mathrm{a}}^2{\mathrm{m}}^2+{\mathrm{b}}^2\right]$ $\Rightarrow n^2=\frac{n^2}{m^2}+1$ $\Rightarrow {\mathrm{m}}^2=\frac{{\mathrm{n}}^2}{{\mathrm{n}}^2-1}$ or ${\mathrm{n}}^2=\frac{{\mathrm{m}}^2}{{\mathrm{m}}^2-1}$