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Miscellaneous Exercise 7(II) · Q131

Q.Find the

(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve: x2/144−y2/25=1x^2/144 - y^2/25 = 1.
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a2=144, b2=25⇒a=12, b=5a^2=144,\,b^2=25 \Rightarrow a=12,\,b=5 (hyperbola, note the MINUS sign).

e2=1+25144=169144⇒e=1312e^2=1+\dfrac{25}{144}=\dfrac{169}{144} \Rightarrow e=\dfrac{13}{12}.

  1. Transverse =24=24, conjugate =10=10.
  2. Foci (±ae,0)=(±13,0)(\pm ae,0)=(\pm13,0).
  3. Directrices x=±ae=±14413x=\pm\dfrac{a}{e}=\pm\dfrac{144}{13}.
  4. Latus rectum =2b2a=256=\dfrac{2b^2}{a}=\dfrac{25}{6}.
  5. Distance between foci =26=26. …
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