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Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
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Q)

State whether the following statement is True or False : If $P$ is a point the ellipse $\large\frac{x^2}{16}+\frac{y^2}{25}$$=1$ whose foci are $S$ and $S'$,then $PS+PS'=8$.

$\begin{array}{1 1}\text{True}\\\text{False}\end{array} $

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A)
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  • In an ellipse sum of the focal distances from the moving point $P$ is $2b$,where $b$ is the distance between the centre and the vertex on the minor axis.
Answer : False
Given equation of the ellipse is $\large\frac{x^2}{16}+\frac{y^2}{25}$$=1$
Hence $b^2=25$
$\Rightarrow b=\pm 5$
$\therefore PS+PS'=2b$
$\Rightarrow 2\times 5=10$
Hence it is a False statement.
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