Q76 / 180 · COMEDK 2019 · Mathematics

The equation $\frac{x^{2}}{2-\lambda}-\frac{y^{2}}{\lambda-5}-1=0$ represents an ellipse if

  • A
    $\lambda>5$
  • Correct answer
    B
    $\lambda < 2$
  • C
    $2 < \lambda < 5$
  • D
    $2>\lambda>5$

Solution

We have, $\begin{aligned} \frac{x^{2}}{2-\lambda}-\frac{y^{2}}{\lambda-5}-1 &=0 \\ \Rightarrow \quad \frac{x^{2}}{2-\lambda}+\frac{y^{2}}{5-\lambda} &=1 \end{aligned}$ It will represent an ellipse, when $$ \begin{array}{ll} & 2-\lambda>0 \text { and } 5-\lambda>0 \\ \Rightarrow \quad & \lambda < 2 \text { and } \lambda < 5 \\ \Rightarrow \quad & \lambda < 2 \end{array} $$

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

More Ellipse Questions