SOLUTION: find the intersection and draw the curves (x-1)^2=y+1, 5x^2-y^2=4x

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Question 1029023: find the intersection and draw the curves (x-1)^2=y+1, 5x^2-y^2=4x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x-1%29%5E2-1
y=x%5E2-2x%2B1-1
y=x%5E2-2x
y%5E2=x%5E4-4x%5E3%2B4x%5E2
Substituting,
5x%5E2-%28x%5E4-4x%5E3%2B4x%5E2%29=4x
5x%5E2-x%5E4%2B4x%5E3-4x%5E2-4x=0
x%5E4-4x%5E3-x%5E2%2B4x=0
x%28x%5E3-4x%5E2-x%2B4%29=0
x%28x%5E3-4x%5E2-x%2B4%29=0
x%28x-4%29%28x-1%29%28x%2B1%29=0
Four solutions,
x=0
x=4
x=1
x=-1
Now use either equation to solve for the corresponding y values.
I'll do one, you do the others,
x=0
y%2B1=%280-1%29%5E2
y%2B1=1
y=0
(0,0)
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