COMEDK · Maths · 14. Ellipse
The equation \(\frac{x^{2}}{2-\lambda}-\frac{y^{2}}{\lambda-5}-1=0\) represents an ellipse if
- A \(\lambda>5\)
- B \(\lambda < 2\)
- C \(2 < \lambda < 5\)
- D \(2>\lambda>5\)
Answer & Solution
Correct Answer
(B) \(\lambda < 2\)
Step-by-step Solution
Detailed explanation
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…
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