Question

Write the equation of the cone z=[square root of:]3x^2+3y^2 in polar coordinates. I don't understand how you convert it.

Answer 1

Remember that in polar you have
\[r^2 = x^2 + y^2\]
So
\[z = \sqrt{3x^2+3y^2}\rightarrow z = \sqrt{3(x^2 + y^2)} = r\sqrt{3} \]