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Angle between Two Line Segments

If the line ...

Question

If the line $L x + m y + n = 0$ cuts the ellipse $(x^{2} / a^{2}) + (y^{2} / b^{2}) = 1$ at points whose eccentric angles differ by $π / 2,$ then find the value of $(a^{2} L^{2} + b^{2} m^{2}) / n^{2}$ .

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Solution

For eccentric angle differ by $\frac{π}{2}$
x will be 0
and y will be $\pm b$
on putting value in equations we get
$\begin{matrix} L^{2} q^{2} = 4 n^{2} a n d m^{2} b^{2} = n^{2} S o, \frac{L^{2} a^{2} + b^{2} m^{2}}{n^{2}} = 5 \end{matrix}$

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