The equation frac{x^{2}}{2-lambda}-frac{y^{2} | vedclass

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(B) The given equation is $\frac{x^{2}}{2-\lambda} - \frac{y^{2}}{\lambda-5} = 1$. For this to represent an ellipse,the equation must be of the form $

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$\lambda < 2$

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(B) The given equation is $\frac{x^{2}}{2-\lambda} - \frac{y^{2}}{\lambda-5} = 1$. For this to represent an ellipse,the equation must be of the form $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ where $a^{2} > 0$ and $b^{2} > 0$. Rewriting the equation: $\frac{x^{2}}{2-\lambda} + \frac{y^{2}}{5-\lambda} = 1$. For this to be an ellipse,both denominators must be positive: $2 - \lambda > 0 \implies \lambda $5 - \lambda > 0 \implies \lambda Taking the intersection of these two conditions,we get $\lambda < 2$.

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

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