Q57 / 125 · BITSAT 2011 · Mathematics

The equation of the ellipse with focus at \(( \pm 5,0)\) and \(x=\frac{36}{5}\) as one directrix is

  • A
    \(\frac{x^2}{36}+\frac{y^2}{25}=1\)
  • Correct answer
    B
    \(\frac{x^2}{36}+\frac{y^2}{11}=1\)
  • C
    \(\frac{x^2}{25}+\frac{y^2}{11}=1\)
  • D
    None of these

Solution

We have ae \(=5\) [Since focus is \(( \pm \mathrm{ae}, 0)\)] and \(\frac{\mathrm{a}}{\mathrm{e}}=\frac{36}{5} \quad\left[\right.\) since directrix is \(\left.\mathrm{x}= \pm \frac{\mathrm{a}}{\mathrm{e}}\right]\) On solving we get \(\mathrm{a}=6\) \(\text { and } \mathrm{e}=\frac{5}{6} \Rightarrow \mathrm{b}^2=\mathrm{a}^2\left(1-\mathrm{e}^2\right)=36\left(1-\frac{25}{36}\right)=11\) Thus, the required equation of the ellipse is \(\frac{x^2}{36}+\frac{y^2}{11}=1\)

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

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