Answer
$\{(0,-5),(0,5)\}$
Work Step by Step
$x^{2}+y^{2}=25$
is a circle, centered at the origin, radius 5.
$25x^{2}+y^{2}=25\qquad/\div 25$
$\displaystyle \frac{x^{2}}{1}+\frac{y^{2}}{25}=1$,
is an ellipse, vertical major axis,
center: origin
a=5, b=1
Intersection points:
$\{(0,-5),(0,5)\}$.
