Answer
$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $\mathrm{x}^{2}+\mathrm{y}^{2}\neq 25$ $\}$
Work Step by Step
Sine is defined everywhere, so no restrictions there.
f is defined for points (x,y) that do not yield zero in the denominator.
We exclude all points for which
$\mathrm{x}^{2}+\mathrm{y}^{2}=25$
This is a circle about the origin of radius $5$.
Since we are excluding it, we graph it with a dashed line.
Domain: all points not lying on circle $\mathrm{x}^{2}+\mathrm{y}^{2}=25$
or, in set notation, $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \ $ $\mathrm{x}^{2}+\mathrm{y}^{2}\neq 25$ $\}$
