The polar equation that corresponds to the rectangular equation $y = x ^ { 2 }$ is

A) $r = - \tan \theta \sec \theta$
B) $r = \tan \theta \sec \theta$
C) $r = \cot \theta \csc \theta$
D) $r = - \cot \theta \csc \theta$
E) $r ^ { 2 } = \tan \theta \sec \theta$

Question

The polar equation that corresponds to the rectangular equation $y = x ^ { 2 }$ is

A) $r = - \tan \theta \sec \theta$
B) $r = \tan \theta \sec \theta$
C) $r = \cot \theta \csc \theta$
D) $r = - \cot \theta \csc \theta$
E) $r ^ { 2 } = \tan \theta \sec \theta$

Quizplus · Accepted Answer

The rectangular equation $y = x^2$ can be converted to polar form using $x = r \cos \theta$ and $y = r \sin \theta$. Substituting these into the equation gives $r \sin \theta = (r \cos \theta)^2$, which simplifies to $r = \tan \theta \sec \theta$.

The Polar Equation That Corresponds to the Rectangular Equation y=x2y = x ^ { 2 }y=x2

The Polar Equation That Corresponds to the Rectangular Equation $y = x ^ { 2 }$