Per the title, does a constant $C$ exist such that the surface of the paraboloid $z=x^2+y^2+C$ is tangent to the surface of the cone $x^2+y^2=z^2$? How would I find this constant?
Thanks a lot!
Per the title, does a constant $C$ exist such that the surface of the paraboloid $z=x^2+y^2+C$ is tangent to the surface of the cone $x^2+y^2=z^2$? How would I find this constant?
Thanks a lot!
Yes. $C=1/4$. You can see this by following up on @Joriki's suggestion and solving the equivalent two dimensional problem: $y=r^2+C=|r|$ $y'=2|r|=1$