Question$r=8 \cos \theta$ is equivalent to what rectangular equation? A. $x^{2}+y^{2}=4^{2}$ B. $(x-8)^{2}+y^{2}=8^{2}$ c. $(x-4)^{2}+y^{2}=4^{2}$ D. $x^{2}+(y-4)^{2}=4^{2}$

Studdy Solution
Rearrange the equation to match one of the given options:
$$x^2 - 8x + y^2 = 0$$
Complete the square for the $x$ terms:
$$(x^2 - 8x + 16) + y^2 = 16$$
This simplifies to:
$$(x - 4)^2 + y^2 = 4^2$$
The rectangular equation is:
$$\boxed{(x - 4)^2 + y^2 = 4^2}$$