If \(\frac{x}{\mathrm{ma}}+\frac{\mathrm{y}}{\mathrm{nb}}=1\) touches the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\),…

\(\mathrm{m}^2=\frac{\mathrm{n}^2}{\mathrm{n}^2-1}\) or \(\mathrm{n}^2=\frac{\mathrm{m}^2}{\mathrm{~m}^2-1}\)

\(\mathrm{m}^2=\frac{\mathrm{n}^2}{\mathrm{n}^2+1}\) or \(\mathrm{n}^2=\frac{\mathrm{m}^2}{\mathrm{~m}^2+1}\)

\(\mathrm{m}^2=\frac{\mathrm{n}^2+1}{\mathrm{n}^2}\) or \( \mathrm{n}^2=\frac{\mathrm{m}^2+1}{\mathrm{~m}^2}\)

\( \mathrm{m}^2=\frac{\mathrm{n}^2-1}{\mathrm{n}^2} \text { or } \mathrm{n}^2=\frac{\mathrm{m}^2-1}{\mathrm{~m}^2}\)