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Axes are coordinate axes, A and L are the ends of major axis and latusrectum. Area of $∆ OAL = 8 sq . units, e = \frac{1}{\sqrt{2}}$ then equation of the ellipse is

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a

$\frac{x^{2}}{16} + \frac{y^{2}}{8} = 1$

b

$\frac{x^{2}}{32} + \frac{y^{2}}{16} = 1$

c

$\frac{x^{2}}{64} + \frac{y^{2}}{32} = 1$

d

$\frac{x^{2}}{8} + \frac{y^{2}}{4} = 1$

answer is B.

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$G i v e n a r e a o f ∆ O A L = 8 a n d e = \frac{1}{\sqrt{2}} \Rightarrow \frac{1}{2} \times a \times \frac{b^{2}}{a} = 8 \Rightarrow b^{2} = 16 \Rightarrow a^{2} (1 - e^{2}) = 16 \Rightarrow a^{2} (1 - \frac{1}{2}) = 16 \Rightarrow a^{2} = 32 ∴ eq u a t i o n o f e l l i p s e i s \frac{x^{2}}{32} + \frac{y^{2}}{16} = 1$

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Axes are coordinate axes, A and L are the ends of major axis and latusrectum. Area of ∆OAL=8 sq.units, e=12then equation of the ellipse is