Question

$$- { x }^{ 2 } + { y }^{ 2 } =289-100$$

Solve for x (complex solution)

$x=-\sqrt{y^{2}-189}$
$x=\sqrt{y^{2}-189}$

Solve for x

$x=\sqrt{y^{2}-189}$
$x=-\sqrt{y^{2}-189}\text{, }|y|\geq 3\sqrt{21}$

Solve for y

$y=\sqrt{x^{2}+189}$
$y=-\sqrt{x^{2}+189}$