PN is the ordinate of any point P on the hyperbola a2x2−b2y2=1 and ∀′ is its transvers axis. If Q divides AP in the ratio a2:b2, then prove that NQ is perpendicular to AprimeP˙

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{P}{N} is the ordinate of any point {P} on the hyperbola {{{x}

Question

$P N$ is the ordinate of any point $P$ on the hyperbola $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ and $\forall^{'}$ is its transvers axis. If $Q$ divides $A P$ in the ratio $a^{2} : b^{2},$ then prove that $N Q$ is perpendicular to $A^{p r i m e} P ˙$

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Emily Discussed

P N

is the ordinate of any point

P

on the hyperbola

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

and

\forall^{'}

is its transvers axis. If

Q

divides

A P

in the ratio

a^{2} : b^{2},

then prove that

N Q

is perpendicular to

A^{p r i m e} P ˙

12 mins ago

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