Chapter 10.4, Problem 4QCE

(a) Suppose that a hyperbola has semifocal axis a and semiconjugate axis $b.$ Then for all points on the hyperbola, the difference of the distance to the farther focus minus the distance to the closer focus is equal to $\text{\_\_\_\_\_\_}\text{.}$

(b) The two standard equations of a hyperbola with semi-focal axis $a$ and semiconjugate axis $b$ are $\text{\_\_\_\_\_\_}$ and $\text{\_\_\_\_\_\_}\text{.}$

(c) Suppose that a hyperbola in standard position has semi-focal axis $a,$ semiconjugate axis $b,$ and foci $\left(\pm c,0\right).$ Then $c$ may be obtained from $a$ and $b$ by the equation $c=\text{\_\_\_\_\_\_}\text{.}$ The equations of the asymptotes of this hyperbola are $y=\pm \text{\_\_\_\_\_\_}.$