Minor Axis of Ellipse

Q. If the minor axis of an ellipse subtends an angle 60° at each focus then the eccentricity of the ellipse is

1. $\frac{\sqrt{3}}{2}$
2. $\frac{1}{\sqrt{2}}$
3. $\frac{2}{\sqrt{3}}$
4. none

Q. If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is inscribed in a rectangle whose length to breadth ratio is $2:1$ in such a manner that it touches the sides of rectangle, then the area of the rectangle is

1. $4\left(\frac{a^2+b^2}{7}\right)$
2. $4\left(\frac{a^2+b^2}{3}\right)$
3. $12\left(\frac{a^2+b^2}{5}\right)$
4. $8\left(\frac{a^2+b^2}{5}\right)$

Q.

If the major axis is "n” times the minor axis of the ellipse, then its eccentricity is

1. $\frac{\sqrt{n-1}}{n}$

2. $\frac{\sqrt{n-1}}{n^2}$

3. $\frac{\sqrt{n^2-1}}{n^2}$

4. $\frac{\sqrt{n^2-1}}{n}$