Find parametric equations for the cylinder $49 x ^ { 2 } + 11 y ^ { 2 } = 539 , - 7 \leq z \leq 11$
A) $x = 11 \cos t , y = 7 \sin t , z = s , 0 \leq t \leq 2 \pi , - 7 \leq s \leq 11$
B) $$x = \sqrt { 11 } \cos t _ { 1 } y = 7 \sin t _ { 1 } \quad z = t _ { 1 } \quad 0 \leq t \leq 2 \pi _ { 1 } - 7 \leq s \leq 11$$
C) $$x = \sqrt { 7 } \cos t _ { 1 } y = 11 \sin t _ { 1 } \quad z = s , \quad 0 \leq t \leq 2 \pi , - 7 \leq s \leq 11$$
D) $x=\sqrt{11} \cos t, y=7 \sin t, \quad z=s, \quad 0 \leq t \leq \pi,-7 \leq s \leq 11$
E) $x=\sqrt{11} \cos t, y=7 \sin t, \quad z=s, \quad 0 \leq t \leq 2 \pi\,-7 \leq s \leq 11$

Question

Find parametric equations for the cylinder $49 x ^ { 2 } + 11 y ^ { 2 } = 539 , - 7 \leq z \leq 11$
A) $x = 11 \cos t , y = 7 \sin t , z = s , 0 \leq t \leq 2 \pi , - 7 \leq s \leq 11$
B) $$x = \sqrt { 11 } \cos t _ { 1 } y = 7 \sin t _ { 1 } \quad z = t _ { 1 } \quad 0 \leq t \leq 2 \pi _ { 1 } - 7 \leq s \leq 11$$
C) $$x = \sqrt { 7 } \cos t _ { 1 } y = 11 \sin t _ { 1 } \quad z = s , \quad 0 \leq t \leq 2 \pi , - 7 \leq s \leq 11$$
D) $x=\sqrt{11} \cos t, y=7 \sin t, \quad z=s, \quad 0 \leq t \leq \pi,-7 \leq s \leq 11$
E) $x=\sqrt{11} \cos t, y=7 \sin t, \quad z=s, \quad 0 \leq t \leq   2 \pi\,-7 \leq s \leq 11$

Quizplus · Accepted Answer

The equation $49x^2 + 11y^2 = 539$ can be rewritten as $\frac{x^2}{(\sqrt{539}/7)^2} + \frac{y^2}{(\sqrt{539}/\sqrt{11})^2} = 1$, which suggests using trigonometric parametrization with $x = \sqrt{11}\cos t$ and $y = 7\sin t$. The range for $t$ is $0 \leq t \leq 2\pi$ to cover the entire cylinder, and $z$ is a free parameter $s$ with the given range $-7 \leq s \leq 11$, matching option E.

Find Parametric Equations for the Cylinder 49x2+11y2=539,−7≤z≤1149 x ^ { 2 } + 11 y ^ { 2 } = 539 , - 7 \leq z \leq 1149x2+11y2=539,−7≤z≤11

Find Parametric Equations for the Cylinder $49 x ^ { 2 } + 11 y ^ { 2 } = 539 , - 7 \leq z \leq 11$