R S Aggarwal Solutions for Exercise 1: EXERCISE

The equation of ellipse whose vertices are at $(\pm 6,0)$ and foci at $(\pm 4,0)$ is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Find $a^2+b^2$.

The equation of ellipse whose vertices are at $(0,\pm 4)$ and foci at $(0,\pm \sqrt{7})$ is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Find $a^2+b^2$.

The equation of ellipse the ends whose major and minor axes are $(\pm 4,0)$ and $(0,\pm 3)$ respectively is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Find $a^2+b^2$.

The length of the major axis of an ellipse is $20 \mathrm{units}$ and its foci are $(\pm 5\sqrt{3},0)$. If the equation of the ellipse is$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, then find $a^2+b^2$.

If the equation of an ellipse, the lengths of whose major and minor axes are $10$ and $8$ units respectively is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Find $a^2+b^2$.

If the equation of an ellipse whose eccentricity is $\frac{2}{3},$ the latus rectum is $5$ and the centre is at the origin is $\frac{4x^2}{a^2}+\frac{4y^2}{b^2}=1$, then find $a^2+b^2$.

If the eccentricity of an ellipse whose latus rectum is one half of its minor axis is $\frac{\sqrt{k}}{2}$, then find $k$. 

If the eccentricity of an ellipse whose latus rectum is one half of its major axis is $\frac{1}{\sqrt{k}}$, then find $k$.