SOLUTION: What are the centers of the equations and their points of intersection? x^2=y+10 y^2+5(x-1)^2=81

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Question 843717: What are the centers of the equations and their points of intersection?
x^2=y+10
y^2+5(x-1)^2=81
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Intersection of an ellipse and a parabola.
1.x%5E2=y%2B10
2.y%5E2%2B5%28x-1%29%5E2=81
From eq. 1,
y=x%5E2-10
y%5E2=x%5E4-20x%5E2%2B100
Substituting into eq. 2,
x%5E4-20x%5E2%2B100%2B5%28x%5E2-2x%2B1%29=81
x%5E4-20x%5E2%2B100%2B5x%5E2-10x%2B5=81
%28x-1%29%28x-4%29%28x%2B2%29%28x%2B3%29=0
.
.
Four solutions:
x-1=0
x=1
Then,
y=1%5E2-10=-9
(1,-9)
and
x-4=0
x=4
Then,
y=4%5E2-10=6
(4,6)
and
x%2B2=0
x=-2
Then,
y=%28-2%29%5E2-10=-6
(-2,-6)
and
x%2B3=0
x=-3
Then
y=%28-3%29%5E2-10=-1
(-3,-1)