KCET · Maths · 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
Given equation can be rewritten as
\[
\frac{x^{2}}{2-\lambda}+\frac{y^{2}}{-\lambda+5}=1
\]
To represents an ellipse,
\[
\begin{array}{ccc}
& 2-\lambda>0 & \text { and } \quad-\lambda+5>0 \\
& \lambda < 2 & \text { and } \quad \lambda < 5 \\
& \lambda < 2
\end{array}
\]
\[
\frac{x^{2}}{2-\lambda}+\frac{y^{2}}{-\lambda+5}=1
\]
To represents an ellipse,
\[
\begin{array}{ccc}
& 2-\lambda>0 & \text { and } \quad-\lambda+5>0 \\
& \lambda < 2 & \text { and } \quad \lambda < 5 \\
& \lambda < 2
\end{array}
\]
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