Answer to Question #105110 in Analytic Geometry for Lazarus Elia P

Question

Find the rectangular equation for z=r^2 cos (2theta)

Name the surface.

Answer 1

$z=r^2cos(2\theta)$

Solution:

$$cos(2\theta)=cos^2\theta-sin^2\theta$$

$z=r^2cos^2 \theta-r^2sin^2\theta$

Since, $x=rcos\theta, y=rsin\theta$

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

Answer:

Hyperbolic paraboloid: $z=x^2-y^2.$