Find a parametrization of the ellipse in which the plane z = 3y intersects the cylinder + = 4, using the polar angle $\theta$ in the xy-plane as the parameter, [0, 2$\pi$] as parameter interval, and ensuring that the ellipse is oriented counterclockwise as viewed from high on the z-axis.
A) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 6 sin($\theta$) k
B) r = 2 cos($\theta$) i - 2 sin($\theta$) j + 6 sin($\theta$) k
C) r = 2 cos($\theta$) i + 2 sin($\theta$) j - 6 sin($\theta$) k
D) r = 2 cos($\theta$) i - 2 sin($\theta$) j - 6 sin($\theta$) k
E) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 3 sin($\theta$) k

Question

Find a parametrization of the ellipse in which the plane z = 3y intersects the cylinder  +  = 4, using the polar angle $\theta$ in the xy-plane as the parameter, [0, 2$\pi$] as parameter interval, and ensuring that the ellipse is oriented counterclockwise as viewed from high on the z-axis.
A) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 6 sin($\theta$) k 
B) r = 2 cos($\theta$) i - 2 sin($\theta$) j + 6 sin($\theta$) k 
C) r = 2 cos($\theta$) i + 2 sin($\theta$) j - 6 sin($\theta$) k 
D) r = 2 cos($\theta$) i - 2 sin($\theta$) j - 6 sin($\theta$) k 
E) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 3 sin($\theta$) k

Quizplus · Accepted Answer

The Answer of Find a parametrization of the ellipse in which the plane z = 3y intersects the cylinder  +  = 4, using the polar angle $\theta$ in the xy-plane as the parameter, [0, 2$\pi$] as parameter interval, and ensuring that the ellipse is oriented counterclockwise as viewed from high on the z-axis.
A) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 6 sin($\theta$) k 
B) r = 2 cos($\theta$) i - 2 sin($\theta$) j + 6 sin($\theta$) k 
C) r = 2 cos($\theta$) i + 2 sin($\theta$) j - 6 sin($\theta$) k 
D) r = 2 cos($\theta$) i - 2 sin($\theta$) j - 6 sin($\theta$) k 
E) r = 2 cos($\theta$) i + 2 sin($\theta$) j + 3 sin($\theta$) k

Find a Parametrization of the Ellipse in Which the Plane θ\thetaθ

Find a Parametrization of the Ellipse in Which the Plane $\theta$