Convert an Equation from Polar to Rectangular Coordinates
-$\mathrm { r } = 8 \cos \theta + 9 \sin \theta$
A) $x ^ { 2 } + y ^ { 2 } = 8 x + 9 y$
B) $x ^ { 2 } - y ^ { 2 } = 8 x + 9 y$
C) $x ^ { 2 } + y ^ { 2 } = 9 x + 8 y$
D) $8 x + 9 y = 0$

Question

Quizplus · Accepted Answer

In polar coordinates, $r = \sqrt{x^2 + y^2}$, $x = r\cos\theta$, and $y = r\sin\theta$. Substituting these into the given equation $r = 8\cos\theta + 9\sin\theta$ gives $r = 8\frac{x}{r} + 9\frac{y}{r}$, which simplifies to $r^2 = 8x + 9y$, or $x^2 + y^2 = 8x + 9y$.

Convert an Equation from Polar to Rectangular Coordinates - r=8cos⁡θ+9sin⁡θ\mathrm { r } = 8 \cos \theta + 9 \sin \thetar=8cosθ+9sinθ

Convert an Equation from Polar to Rectangular Coordinates
- $\mathrm { r } = 8 \cos \theta + 9 \sin \theta$