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Conic Section

Question
CBSEENMA11015593
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For the Hyperbola fraction numerator straight x squared over denominator cos squared space straight alpha end fraction space minus space fraction numerator straight y squared over denominator begin display style sin squared end style begin display style space end style begin display style straight alpha end style end fraction space equals 1 which of the following remains constant when α varies?

  • Eccentricity

  • Directrix

  • Abscissae of vertices

  • Abscissae of foci

Solution

D.

Abscissae of foci

a2 = cos2α and b2 = sin2α
coordinates of focii are (± ae, 0)
∴ b2= a2(e2– 1) ⇒ e = secα.
Hence abscissae of foci remain constant when α varies.

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