Find an Equation for the Surface Obtained by Rotating the Parabola y = x2 About the y-axis

We thoroughly check each answer to a question to provide you with the most correct answers. Found a mistake? Tell us about it through the REPORT button at the bottom of the page. Ctrl+F (Cmd+F) will help you a lot when searching through such a large set of questions.

Find an equation for the surface obtained by rotating the parabola y = x^2 about the y-axis.

Answer: y = x^2 + z^2

Explanation

Rotate y = x^2 around the y-axis

When rotated the traces parallel to the xz-plane are circles. So the equation should be that of a circle when y = k.

k = x^2

we just have to add a + z^2

y = x^2 + z^2

find an equation for the surface obtained by rotating the parabola y = x2 about the y-axis.

Was this helpful?