Q68 / 160 · AP EAMCET 2003 · Mathematics

The eccentricity of the ellipse $9 x^2+5 y^2-18 x-20 y-16=0$, is :

  • A
    $\frac{1}{2}$
  • Correct answer
    B
    $\frac{2}{3}$
  • C
    $\frac{3}{2}$
  • D
    2

Solution

Equation of ellipse is $9 x^2+5 y^2-18 x-20 y-16=0$ $\Rightarrow \quad 9\left(x^2-2 x\right)+5\left(y^2-4 y\right)=16$ $\Rightarrow 9\left(x^2-2 x+1\right)+5\left(y^2-4 y+4\right)=16+9+20$ $\Rightarrow \quad 9(x-1)^2+5(y-2)^2=45$ $\Rightarrow \quad \frac{(x-1)^2}{5}+\frac{(y-2)^2}{9}=1$ Here $a^2=5, b^2=9$ eccentricity, $e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{5}{9}}=\frac{2}{3}$

Hence, the correct answer is option: 'B'.

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