The equation of hyperbola whose eccentricity is $\frac{5}{3}$ and distance between the foci is 10 units is

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Aicharya · Accepted Answer

Given, $e=5 / 3$ and $2 a e=10$ $\Rightarrow \quad 2 a\left(\frac{5}{3}ight)=10 \Rightarrow a=3$ $\Rightarrow \quad(a e)^2=a^2+b^2 \Rightarrow(5)^2=3^2+b^2$ $\Rightarrow b^2=25-9=16$ $	herefore$ Equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$ $\Rightarrow \quad 16 x^2-9 y^2=144$

The equation of hyperbola whose eccentricity is $\frac{5}{3}$ and distance between the foci is 10 units is

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