Chapter 10.4, Problem 3QCE

(a) Suppose that an ellipse has semimajor axis $a$ and semiminor axis $b$ Then for all points on the ellipse, the sum of the distances to the foci is equal to $\text{\_\_\_\_\_\_}.$

(b) The two standard equation of an ellipse with semi major axis $a$ and semiminor axis $b$ are $\text{\_\_\_\_\_\_}$ and $\text{\_\_\_\_\_\_}\text{.}$

(c) Suppose that an ellipse has semimajor axis $a,$ semiminor axis $b,$ and foci $\left(\pm c,0\right).$ Then $c$ may be obtained from $a\text{and}b$ by the equation $c=\text{\_\_\_\_\_\_}\text{.}$