Question

If the axes of the ellipse are coordinate axes and A and B are the ends of major axis and minor axis respectively.If the area of $△$OAB is 16 sq units, e = $\frac{\sqrt{3}}{2}$ then the equation of the ellipse is

• A. $\frac{x^2}{32}+\frac{y^2}{8}$=1
• B. $\frac{x^2}{64}+\frac{y^2}{16}$=1
• C. $\frac{x^2}{64}+\frac{y^2}{8}$=1
• D. $\frac{x^2}{64}+\frac{y^2}{32}$=1

Answer 1

The correct option is B

$\frac{x^2}{64}+\frac{y^2}{16}$=1

e = $\frac{\sqrt{3}}{2}$

$\frac{1}{2}$*a*b=16

$\Rightarrow$ab=32

$b^2$=$a^2(1-e^2)$

$b^2$=$a^2(1-\frac{3}{4})$=$a^2\left(\frac{1}{4}\right)\Rightarrow 4b^2$=$a^2$

2b.b=32$\Rightarrow b^2$=16

a=2b,a=8

$\frac{x^2}{64}+\frac{y^2}{16}$=1