Chapter 11, Problem 67RE

(a)

To determine

To draw: The graphs of the family of ellipses $\frac{x^2}{16+k^2}+\frac{y^2}{k^2}=1$ for $k=1,2,4\text{and}8$.

(b)

To determine

To prove: All the family of ellipses $\frac{x^2}{16+k^2}+\frac{y^2}{k^2}=1$ have the same foci.