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  4. If the area of the Ellipse is (x2/25)+(y2/λ2)=1 is 20 π square units, then λ is

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Q. If the area of the Ellipse is $\frac{x^{2}}{25}+\frac{y^{2}}{\lambda^{2}}=1$ is $20 \pi$ square units, then $\lambda$ is

KCETKCET 2021Conic Sections

Solution:

$\frac{ x ^{2}}{25}+\frac{ y ^{2}}{\lambda^{2}}=1$
$\pi ab =\pi \cdot 5 \cdot|\lambda|=20\, \pi$
$|\lambda|=4 \Rightarrow \lambda=\pm 4$