points of intersection between cone and paraboloid

Hey everyone, I need to find the points of intersection between the cone $\displaystyle z=\sqrt(x^2+y^2) $and $\displaystyle z=2-x^2-y^2 $

So, what I did was

$\displaystyle 2-x^2-y^2=\sqrt(x^2+y^2)$

$\displaystyle (2-x^2-y^2)(2-x^2-y^2)=x^2+y^2$

$\displaystyle x^4+y^4-5*x^2-5*y^2+2*x^2*y^2+4=0$

The problem is, I don't know what to do for now, can any one give me any tips?

Best Regards

Junks

Re: points of intersection between cone and paraboloid

Quote:

Originally Posted by

**junkwisch** Hey everyone, I need to find the points of intersection between the cone $\displaystyle z=\sqrt(x^2+y^2) $and $\displaystyle z=2-x^2-y^2 $

So, what I did was

$\displaystyle 2-x^2-y^2=\sqrt(x^2+y^2)$

$\displaystyle (2-x^2-y^2)(2-x^2-y^2)=x^2+y^2$

$\displaystyle x^4+y^4-5*x^2-5*y^2+2*x^2*y^2+4=0$

The problem is, I don't know what to do for now, can any one give me any tips?

Best Regards

Junks

$z = \sqrt{x^2+y^2}$

$z = 2 - x^2 - y^2$

$z = 2 - z^2$