I have a problem where i need to

find the equation for surface of revolution if the generating curvey = 2x + 1, is revolved about the y axis

The book gives this formula for revolving around the y axis

$\displaystyle x^2 + z^2 = [ r(y)]^2$

So, wouldnt i just plug y in and square it?

most of the problems have been done this way

Problem is i dont get the right answer.

the answer is

$\displaystyle 4x^2 -y^2 + 4z^2 + 2y - 1 =0$

What do i need to do?

Thank you