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Exercise 7.3 · Q71

Q.Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola y225−x2144=1\dfrac{y^2}{25} - \dfrac{x^2}{144} = 1.

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Here A2=25, B2=144⇒A=5, B=12A^2=25,\,B^2=144 \Rightarrow A=5,\,B=12; transverse axis along YY.

e2=1+14425=16925⇒e=135e^2=1+\dfrac{144}{25}=\dfrac{169}{25} \Rightarrow e=\dfrac{13}{5}.

  • Transverse axis =10=10; conjugate axis =24=24.
  • Foci (0,±Ae)=(0,±13)(0,\pm Ae)=(0,\pm13).
  • Directrices y=±Ae=±2513y=\pm\dfrac{A}{e}=\pm\dfrac{25}{13}. …
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