Find an equivalent equation in polar coordinates.
-$$x ^ { 2 } + y ^ { 2 } - 4 x = 0$$
A) $r \sin ^ { 2 } \theta = 4 \cos \theta$
B) $r \cos ^ { 2 } \theta = 4 \sin \theta$
C) $r = 4 \cos \theta$
D) $r = 4 \sin \theta$

Question

Quizplus · Accepted Answer

The given equation in Cartesian coordinates is $x^2 + y^2 - 4x = 0$. To convert it into polar coordinates, we use the relations $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the equation gives $r^2 \cos^2 \theta + r^2 \sin^2 \theta - 4r \cos \theta = 0$. Simplifying using the identity $\cos^2 \theta + \sin^2 \theta = 1$, we get $r^2 - 4r \cos \theta = 0$, or $r = 4 \cos \theta$, which matches option C.

Find an Equivalent Equation in Polar Coordinates x2+y2−4x=0x ^ { 2 } + y ^ { 2 } - 4 x = 0x2+y2−4x=0

Find an Equivalent Equation in Polar Coordinates $x ^ { 2 } + y ^ { 2 } - 4 x = 0$