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Exercise 7.3 · Q72

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 x2100−y225=+1\dfrac{x^2}{100} - \dfrac{y^2}{25} = +1.

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a2=100, b2=25⇒a=10, b=5a^2=100,\,b^2=25 \Rightarrow a=10,\,b=5.

e2=1+25100=54⇒e=52e^2=1+\dfrac{25}{100}=\dfrac54 \Rightarrow e=\dfrac{\sqrt5}{2}.

  • Transverse axis =20=20; conjugate axis =10=10.
  • Foci (±ae,0)=(±10⋅52,0)=(±55,0)(\pm ae,0)=\left(\pm10\cdot\dfrac{\sqrt5}{2},0\right)=(\pm5\sqrt5,0).
  • Directrices x=±ae=±105/2=±45x=\pm\dfrac{a}{e}=\pm\dfrac{10}{\sqrt5/2}=\pm4\sqrt5. …
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