Replace the Cartesian equation with an equivalent polar equation.
-$$x ^ { 2 } + ( y - 25 ) ^ { 2 } = 625$$
A) $r = 50 \sin \theta$
B) $\mathrm { r } ^ { 2 } = 50 \cos \theta$
C) $r = 25 \sin \theta$
D) $r = 50 \cos \theta$

Question

Quizplus · Accepted Answer

The given equation is a circle with a center at (0, 25) and a radius of 25. In polar coordinates, this translates to $r = 50 \sin \theta$ because the circle's equation in polar form is $r = 2a \sin \theta$ or $r = 2a \cos \theta$, where $a$ is the radius and the circle is shifted along the y-axis. Here, $2a = 50$, indicating a shift along the y-axis, matching with $\sin \theta$.

Replace the Cartesian Equation with an Equivalent Polar Equation x2+(y−25)2=625x ^ { 2 } + ( y - 25 ) ^ { 2 } = 625x2+(y−25)2=625

Replace the Cartesian Equation with an Equivalent Polar Equation $x ^ { 2 } + ( y - 25 ) ^ { 2 } = 625$