The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ).
-$$y ^ { 2 } = 16 x$$
A) $r \sin ^ { 2 } \theta = 16 \cos \theta$
B) $\sin ^ { 2 } \theta = 16 \mathrm { r } \cos \theta$
C) $r ^ { 2 } \sin ^ { 2 } \theta = 16 \cos \theta$
D) $\sin ^ { 2 } \theta = 16 r ^ { 2 } \cos \theta$

Question

Quizplus · Accepted Answer

To convert the given rectangular coordinate equation $y^2 = 16x$ to polar coordinates, use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the given equation yields $r^2\sin^2\theta = 16r\cos\theta$. Dividing both sides by $r$ (assuming $r \neq 0$) simplifies to $r\sin^2\theta = 16\cos\theta$, which matches choice A.

The Letters X and Y Represent Rectangular Coordinates y2=16xy ^ { 2 } = 16 xy2=16x

The Letters X and Y Represent Rectangular Coordinates $y ^ { 2 } = 16 x$