Find an equation in cylindrical coordinates for the equation given in rectangular coordinates. $$9 x ^ { 2 } + 9 y ^ { 2 } = 8 x$$
A) $r ^ { 2 } = \frac { 8 } { 9 } \sin \theta$
B) $r = \frac { 8 } { 9 } \sin \theta$
C) $r = \frac { 8 } { 9 } \cos ^ { - 1 } \theta$
D) $r = \frac { 8 } { 9 } \cos \theta$
E) $r = \frac { 9 } { 8 } \cos \theta$

Question

Quizplus · Accepted Answer

We can rewrite the equation in cylindrical coordinates using the conversion formulas $x = r\cos	heta$ and $y=r\sin	heta$:

\begin{align*}
9x^2+9y^2 &= 8x\
9(r\cos	heta)^2 + 9(r\sin	heta)^2 &= 8(r\cos	heta)\
9r^2(\cos^2	heta + \sin^2	heta) &= 8r\cos	heta\
r &= \frac{8\cos	heta}{9}
\end{align*}

So the equation in cylindrical coordinates is $r = \frac{8}{9}\cos	heta$. The correct choice is $\boxed{	ext{(D)}}$.

Find an Equation in Cylindrical Coordinates for the Equation Given 9x2+9y2=8x9 x ^ { 2 } + 9 y ^ { 2 } = 8 x9x2+9y2=8x

Find an Equation in Cylindrical Coordinates for the Equation Given $9 x ^ { 2 } + 9 y ^ { 2 } = 8 x$