CPM Homework Help : PC3 Problem 10-78

Decide whether each of the following hyperbolas is oriented horizontally or vertically. That is, decide whether the transverse axis is horizontal or vertical. How can you tell?

$\frac { x ^ { 2 } } { 10 } - \frac { y ^ { 2 } } { 5 }= 1$
Hint (a):
Notice which term ( $x^{2}$ or $y^{2}$ ) is negated. What does this indicate about the orientation?
More Help (a):
If you can't remember which term corresponds to which orientation, try setting either $x$ or $y$ to $0$ . In which case is the function defined?
Answer (a):
The transverse axis is horizontal.

$\frac { y ^ { 2 } } { 6 } - \frac { x ^ { 2 } } { 16 }= 1$
Hint (b):
See part (a).

$\frac { ( y - 2 ) ^ { 2 } } { 10 } - \frac { ( x - 5 ) ^ { 2 } } { 7 }= 1$
Hint (c):
See part (a).