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Exercise 7.3 · Q69

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 x2−y2=16x^2 - y^2 = 16.

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x2−y2=16⇒x216−y216=1x^2-y^2=16 \Rightarrow \dfrac{x^2}{16}-\dfrac{y^2}{16}=1. So a2=b2=16⇒a=b=4a^2=b^2=16 \Rightarrow a=b=4 — a rectangular hyperbola.

e2=1+1616=2⇒e=2e^2=1+\dfrac{16}{16}=2 \Rightarrow e=\sqrt2.

  • Transverse axis =8=8; conjugate axis =8=8.
  • Foci (±ae,0)=(±42,0)(\pm ae,0)=(\pm4\sqrt2,0).
  • Directrices x=±ae=±42=±22x=\pm\dfrac{a}{e}=\pm\dfrac{4}{\sqrt2}=\pm2\sqrt2. …
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