If B and B - are the ends of the minor axis and S and S - are foci of the ellipse x 2-25- y 2-9-1- then the area of the rhombus SBS - B - will beA- 12 sq- unitB- 48 sq- unitC- 24 sq- unitD- 36 sq- unit

The correct option is C 24 sq. unit nbsp; nbsp; nbsp; x^225+y^29=1 e=√(1 925)=45 S=(ae,0)=(5×45,0)=(4,0) Area of Rhombus =4 area Δ BOS =4 (12× OS× OB ...

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Standard XII

Physics

Vector Addition

If B and B ' ...

Question

If $B$ and $B^{'}$ are the ends of the minor axis and $S$ and $S^{'}$ are foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , then the area of the rhombus $S B S^{'} B^{'}$ will be

12 sq. unit

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48 sq. unit

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24 sq. unit

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36 sq. unit

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Solution

The correct option is C $24 sq. unit$

$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 e = \sqrt{1 - \frac{9}{25}} = \frac{4}{5}$
$S = (a e, 0) = (5 \times \frac{4}{5}, 0) = (4, 0)$

Area of Rhombus $= 4 area Δ B O S$
$= 4 (\frac{1}{2} \times O S \times O B)$
$= 4 (\frac{1}{2} \times 4 \times 3)$
$= 24 sq. units$

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If B and B′ are the ends of the minor axis and S and S′ are foci of the ellipse x225+y29=1, then the area of the rhombus SBS′B′ will be

The correct option is C 24 sq. unit x225+y29=1e=√1−925=45 S=(ae,0)=(5×45,0)=(4,0) Area of Rhombus =4 area ΔBOS =4(12×OS×OB) =4(12×4×3) =24 sq. units

If $B$ and $B^{'}$ are the ends of the minor axis and $S$ and $S^{'}$ are foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1$ , then the area of the rhombus $S B S^{'} B^{'}$ will be