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Exercise 7.3 · Q67

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 21x2−4y2=8421x^2 - 4y^2 = 84.

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21x2−4y2=84⇒x24−y221=121x^2-4y^2=84 \Rightarrow \dfrac{x^2}{4}-\dfrac{y^2}{21}=1. So a2=4, b2=21⇒a=2, b=21a^2=4,\,b^2=21 \Rightarrow a=2,\,b=\sqrt{21}.

e2=1+214=254⇒e=52e^2=1+\dfrac{21}{4}=\dfrac{25}{4} \Rightarrow e=\dfrac52.

  • Transverse axis =4=4; conjugate axis =221=2\sqrt{21}.
  • Foci (±ae,0)=(±5,0)(\pm ae,0)=(\pm5,0).
  • Directrices x=±ae=±45x=\pm\dfrac{a}{e}=\pm\dfrac45. …
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