Question

The ellipse $E_1:\frac{x^2}{9}+\frac{y^2}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point $\left(0,4\right)$ circumscribes the rectangle $R$ . The length (in units) of the major axis of ellipse $E_2$ is

Answer 1

Answer: 8

Let the ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

As it is passing through $\left(0,4\right)$ and $\left(3,2\right)$ . So, $b^2=16$ and $\frac{9}{a^2}+\frac{4}{16}=1$ or $a^2=12$
So, the length of major axis $=2b=8$