Answer
See graph and explanations.
Work Step by Step
(a )The top halves of the family of ellipses are shown in the figure.
(b) Members of this family of ellipses have a common major axis (for $k\gt1$), while they differ in the lengths of minor axes. To explain this, divide 100 on both sides of the equation in (a), we get
$\frac{x^2}{10^2}+\frac{y^2}{(10/\sqrt k)^2}=1$, compare this with a standard equation, we have $a=10, b=\frac{10}{\sqrt k}$. With an increasing $k$ value, the length of the minor axis $b$ will become smaller as shown in the figure.
