Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. $z = 9 x ^ { 2 } + 9 y ^ { 2 } - 2$
A) $z = 9 r + 2$
B) $z = 9 r ^ { 2 } - 2$
C) $z ^ { 2 } = 9 r - 2$
D)$z = \frac { 9 } { 2 } r ^ { 2 } + 2$
E)$z = \frac { 9 } { 2 } r ^ { 2 } - 2$

Question

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. $z = 9 x ^ { 2 } + 9 y ^ { 2 } - 2$
A) $z = 9 r + 2$
B) $z = 9 r ^ { 2 } - 2$
C) $z ^ { 2 } = 9 r - 2$ 
D)$z = \frac { 9 } { 2 } r ^ { 2 } + 2$
E)$z = \frac { 9 } { 2 } r ^ { 2 } - 2$

Quizplus · Accepted Answer

In cylindrical coordinates, we have $x = r \cos 	heta$ and $y = r \sin 	heta$. Substituting these values in the given equation, we get 
$$z = 9 r^2 \cos^2 	heta + 9 r^2 \sin^2 	heta - 2 = 9r^2 - 2$$
Therefore, the equation in cylindrical coordinates is $z = 9 r^2 - 2$, which is choice (B).

Find an Equation in Cylindrical Coordinates for the Equation Given z=9x2+9y2−2z = 9 x ^ { 2 } + 9 y ^ { 2 } - 2z=9x2+9y2−2

Find an Equation in Cylindrical Coordinates for the Equation Given $z = 9 x ^ { 2 } + 9 y ^ { 2 } - 2$