Question 250436

1.{{{x^2+y^2=25}}}
2.{{{x^2-y=5}}}
This solves the intersection of a parabola and a circle. 
From 2,
{{{x^2=y+5}}}
Subsitute into 1.
{{{x^2+y^2=25}}}
{{{(y+5)+y^2=25}}}
{{{y^2+y-20=0}}}
{{{(y+5)(y-4)=0}}}
Two solutions:
y+5=0
y=-5
Then 
{{{x^2=y+5}}}
{{{x^2=5+5=0}}}
{{{x=0}}}
.
.
.
{{{y-4=0}}}
{{{y=4}}}
Then
{{{x^2=y+5}}}
{{{x^2=4+5=9}}}
{{{x=3}}} and {{{x=-3}}}
The intersection points are then
(3,4), (-3,4), and (0,-5)

{{{ graph( 300, 300, -6, 6, -6, 6, x^2-5, sqrt(25-x^2), -sqrt(25-x^2)) }}}