Convert an Equation from Rectangular to Polar Coordinates
-$2 x - 5 y + 12 = 0$
A) $r = \frac { - 12 } { ( 2 \cos \theta - 5 \sin \theta ) }$
B) $r = \frac { - 12 } { ( 2 \sin \theta - 5 \cos \theta ) }$
C) $2 \cos \theta - 5 \sin \theta = - 12$
D) $2 \cos \theta - 5 \sin \theta = 12$

Question

Quizplus · Accepted Answer

To convert the given rectangular equation $2x - 5y + 12 = 0$ to polar coordinates, we use the relationships $x = r\cos\theta$ and $y = r\sin\theta$. Substituting these into the equation gives $2r\cos\theta - 5r\sin\theta + 12 = 0$, which can be rearranged to $r = \frac{-12}{2\cos\theta - 5\sin\theta}$, matching option A.

Convert an Equation from Rectangular to Polar Coordinates - 2x−5y+12=02 x - 5 y + 12 = 02x−5y+12=0

Convert an Equation from Rectangular to Polar Coordinates
- $2 x - 5 y + 12 = 0$