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JEE Main 2007
Exam
JEE Main
Year
2007
Subject
Mathematics
Chapter
Hyperbola

JEE Main 2007 · Mathematics · Hyperbola

For the hyperbola (x^2)/( ^2 α)-(y^2)/( ^2 α)=1 , which of the...

For the hyperbola x2cos⁡2α−y2sin⁡2α=1\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{\sin ^2 \alpha}=1, which of the following remains constant when α\alpha varies?

Options

  1. Aeccentricity
  2. Bdirectrix
  3. Cabscissae of vertices
  4. Dabscissae of foci

Correct answer

D. abscissae of foci

Step-by-step solution

a2=cos⁡2αa^2=\cos ^2 \alpha and b2=sin⁡2αb^2=\sin ^2 \alpha Coordinates of focii are (±ae,0)(\pm a e, 0) ∴b2=a2(e2−1)⇒e=sec⁡α\therefore b^2=a^2\left(e^2-1\right) \Rightarrow e=\sec \alpha. Hence abscissae of foci remain constant when α\alpha varies.
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