Which answer is a rectangular form of the given polar equation? $r = 10 \cos \theta$
A) $( x - 5 ) ^ { 2 } + y ^ { 2 } = 25$
B) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 25$
C) $( x + 5 ) ^ { 2 } + y ^ { 2 } = 5$
D) $x ^ { 2 } + ( y + 5 ) ^ { 2 } = 25$
E) $x ^ { 2 } + ( y - 5 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

The polar equation $r = 10 \cos \theta$ can be converted to rectangular form using the identities $r^2 = x^2 + y^2$ and $x = r \cos \theta$. Substituting $r = 10 \cos \theta$ into $x = r \cos \theta$ gives $x = 10 \cos^2 \theta$. Using the double angle identity, $\cos^2 \theta = \frac{1 + \cos(2\theta)}{2}$, and recognizing that in rectangular coordinates, $x = r \cos \theta$, we simplify to find an equation in terms of $x$ and $y$. The correct transformation leads to $(x - 5)^2 + y^2 = 25$, which is a circle centered at (5, 0) with a radius of 5, matching the original polar equation's description.

Which Answer Is a Rectangular Form of the Given Polar r=10cos⁡θr = 10 \cos \thetar=10cosθ

Which Answer Is a Rectangular Form of the Given Polar $r = 10 \cos \theta$