Mathematics - Ellipse Question with Solution | TestHub

MathematicsEllipseGeneralMedium2 minPYQ_2019

MathematicsMediumstatement

Let $S$ and $S^{'}$ be the foci of an ellipse and $B$ be any one of the extremities of its minor axis. If $Δ S^{'} B S$ is a right angled triangle with right angle at $B$ and area $(Δ S^{'} B S) = 8 sq . units$ , then the length of a latus rectum of the ellipse is :

Options:

Answer:

Solution:

Given that,

$∠ S B S^{'} = \frac{π}{2}$

$\Rightarrow ∠ O B S = \frac{π}{4}$

$\Rightarrow b = a e . . . (i)$

Also, area $(∆ S B S^{'}) = 8$

$\Rightarrow \frac{1}{2} . 2 a e . b = 8$

$\Rightarrow a e b = 8 . . . (i i)$

From equations $(i) & (i i)$ ,

$b^{2} = 8$ and $a^{2} = b^{2} + a^{2} e^{2} = 8 + 8 = 16$

$\Rightarrow b = 2 \sqrt{2}$ and $a = 4$

Thus, the length of the latus rectum is $\frac{2 b^{2}}{a} = \frac{16}{4} = 4$

Stream:JEESubject:MathematicsTopic:EllipseSubtopic:General

⏱ 2mℹ️ Source: PYQ_2019

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