Find the equation of the circle that passes through the origin and has its center at ( $-$ 27, 36). A) x ² + y ² + 27 x + 36 y = 0 B) x 2 + y 2 + 27 x $-$ 36 y = 0 C) x ² + y ² + 54 x + 72 y = 0 D) x 2 + y 2 + 54 x $-$ 72 y = 0 E) x 2 + y 2 + 72 x $-$ 54 y = 0

Question

Quizplus · Accepted Answer

A circle with center (h,k) and radius r has an equation of the form (x-h)^(2)+(y-k)^(2)=r^(2). 
Since the circle passes through the origin, we know that (0,0) must satisfy this equation:
(0-(-27))^(2)+(0-36)^(2)=r^(2)
756+1296=r^(2)
r^(2)=2052
Thus, the equation of the circle is:
(x+27)^(2)+(y-36)^(2)=2052
which can be rewritten as:
x^(2)+y^(2)+54x-72y=0.

Find the Equation of the Circle That Passes Through the Origin