Convert the rectangular equation to polar form.Assume a 0,r 0. $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$
A) $r = 5 a \sin \theta$
B) $r = 5 a \cot \Theta$
C) $r = 5 \operatorname { acsc } \theta$
D) $r = 5 a \cos \theta$
E) $r = 5 \operatorname { asec } \theta$

Question

Convert the rectangular equation to polar form.Assume a > 0,r > 0.​ $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$ ​
A) $r = 5 a \sin \theta$
B) $r = 5 a \cot \Theta$
C) $r = 5 \operatorname { acsc } \theta$
D) $r = 5 a \cos \theta$
E) $r = 5 \operatorname { asec } \theta$

Quizplus · Accepted Answer

The given rectangular equation is $x^2 + y^2 - 5ax = 0$. In polar coordinates, $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $r^2\cos^2\theta + r^2\sin^2\theta - 5ar\cos\theta = 0$. Since $r^2(\cos^2\theta + \sin^2\theta) = r^2$, the equation simplifies to $r^2 - 5ar\cos\theta = 0$, or $r = 5a\cos\theta$, which corresponds to option D.

Convert the Rectangular Equation to Polar Form x2+y2−5ax=0x ^ { 2 } + y ^ { 2 } - 5 a x = 0x2+y2−5ax=0

Convert the Rectangular Equation to Polar Form $x ^ { 2 } + y ^ { 2 } - 5 a x = 0$