If the line lx+my+n=0 cuts the ellipse a2x2+b2y2=1 ponts whose eccentric angles differ by 2π , then find the value of n2a2l2+b2m2

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If the line {l}{x}+{m}{y}+{n}={0} cuts the ellipse {{{x}^{{{2}

Question

If the line $l x + m y + n = 0$ cuts the ellipse $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ ponts whose eccentric angles differ by $\frac{π}{2}$ , then find the value of $\frac{a ^{2} l ^{2} + b ^{2} m ^{2}}{n ^{2}}$

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Michael Discussed

If the line

l x + m y + n = 0

cuts the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

ponts whose eccentric angles differ by

\frac{π}{2}

, then find the value of

\frac{a ^{2} l ^{2} + b ^{2} m ^{2}}{n ^{2}}

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Question Text

If the line

l x + m y + n = 0

cuts the ellipse

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

ponts whose eccentric angles differ by

\frac{π}{2}

, then find the value of

\frac{a ^{2} l ^{2} + b ^{2} m ^{2}}{n ^{2}}