If α$$+$$β$$=$$π then the chord joining the points α and β for the hyperbola $$x2a2$$−$$y2b2=1$$ passes through

Hyperbola in conic sections

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Question

$If α + β = π then the chord joining the points α and β for the hyperbola \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 passes through$

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Solution

$Points on hyperbola P (a \sec α, b \tan α) and Q (a \sec β, b \tan β)$
$β = π - α$
$∴ Q (a \sec (π - α), b \tan (π - α)) or Q (- a \sec α, - b \tan α)$
$Clearly points P and Q are symmetric about origin. Hence chord joining P and Q passes through origin.$

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