Convert the rectangular equation to polar form.Assume a 0,r 1. $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$
A) $r = 3 a \sin \theta$
B) $r = 3 a \cot \Theta$
C) $r = 3 a \cos \theta$
D) $r = 3 \operatorname { asec } \theta$
E) $r = 3 \operatorname { acsc } \theta$

Question

Convert the rectangular equation to polar form.Assume a > 0,r > 1.​ $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$ ​
A) $r = 3 a \sin \theta$
B) $r = 3 a \cot \Theta$
C) $r = 3 a \cos \theta$
D) $r = 3 \operatorname { asec } \theta$
E) $r = 3 \operatorname { acsc } \theta$

Quizplus · Accepted Answer

The given equation in rectangular coordinates is $x^2 + y^2 - 3ay = 0$. In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $r^2\cos^2\theta + r^2\sin^2\theta - 3ar\sin\theta = 0$. Since $r^2(\cos^2\theta + \sin^2\theta) = r^2$, the equation simplifies to $r^2 - 3ar\sin\theta = 0$, or $r = 3a\sin\theta$, which matches choice A.

Convert the Rectangular Equation to Polar Form x2+y2−3ay=0x ^ { 2 } + y ^ { 2 } - 3 a y = 0x2+y2−3ay=0

Convert the Rectangular Equation to Polar Form $x ^ { 2 } + y ^ { 2 } - 3 a y = 0$