Question

Area of the rectangle formed by the ends of latusrecta of the Ellipse $4x^2+9y^2$ = 144 is

• A. $\frac{32\sqrt{5}}{3}$
• B. $\frac{64\sqrt{5}}{3}$
• C. $\frac{16\sqrt{5}}{3}$
• D. $\frac{32\sqrt{3}}{5}$

Answer 1

The correct option is B

$\frac{64\sqrt{5}}{3}$

$4x^2+9y^2$ = 14y, a=6

$\frac{x^2}{36}+\frac{y^2}{16}$ = 1, b=4

e = $\sqrt{1-\frac{16}{36}}$ = $\frac{\sqrt{5}}{3}$

Length of the lactus rectum,$S{S}^1$ = $\frac{2X16}{6}$ = $\frac{16}{3}$

Area = $4\sqrt{5}x\frac{16}{3}$ = $\frac{64\sqrt{5}}{3}$