#1) find all POIs: 3*x-y==-2, 2*x^2-y==0
var('y')
show(solve(3*x-y==-2,y))
show(solve(2*x^2-y==0,y))
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solve([3*x-y==-2, 2*x^2-y==0],x,y)
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plot([3*x+2,2*x^2],-1,3)
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plot([3*x+2,2*x^2],-1,3,aspect_ratio=1)
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#2) Find all POIs: x^2+y^2==13, x^2-y==7
show(solve(x^2+y^2==13,y))
show(solve(x^2-y==7,y))
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solve([x^2+y^2==13,x^2-y==7],x,y)
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plot([-sqrt(13-x^2),sqrt(13-x^2),x^2-7],-sqrt(13),sqrt(13),aspect_ratio=1)
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#3) Find all POIs: x^2-y^2==4, y==x^2
solve([x^2-y^2==4,y==x^2],x,y)
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show(solve(x^2-y^2==4,y))
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a=plot([-sqrt(x^2-4)],-4,-2,color='red')
b=plot([-sqrt(x^2-4)],2,4,color='red')
c=plot([sqrt(x^2-4)],-4,-2,color='green')
d=plot([sqrt(x^2-4)],2,4,color='green')
e=plot([x^2],-4,4,color='orange')
show(a+b+c+d+e,aspect_ratio=1)
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