Find a polar equation for the parametric equations.
$$x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )$$
A) $y = x \tan \theta$
B) $r = \sqrt { \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 } }$
C) $x ^ { 2 } + y ^ { 2 } = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$
D) $r = \left[ f _ { 1 } ( \theta ) \right] ^ { 2 } + \left[ f _ { 2 } ( \theta ) \right] ^ { 2 }$

Question

Quizplus · Accepted Answer

The correct polar equation that relates to the given parametric equations $x = f_1(\theta)$ and $y = f_2(\theta)$ is $r = \sqrt{[f_1(\theta)]^2 + [f_2(\theta)]^2}$. This is because in polar coordinates, $r = \sqrt{x^2 + y^2}$, and substituting $x = f_1(\theta)$ and $y = f_2(\theta)$ gives the correct formula.

Find a Polar Equation for the Parametric Equations x=f1(θ),y=f2(θ)x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )x=f1​(θ),y=f2​(θ)

Find a Polar Equation for the Parametric Equations $x = f _ { 1 } ( \theta ) , y = f _ { 2 } ( \theta )$