Find the general form of the equation of the the circle.
-Center at the point $( 2 , - 3 )$; containing the point $( 5 , - 3 )$
A) $x ^ { 2 } + y ^ { 2 } + 4 x - 6 y + 22 = 0$
B) $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y + 22 = 0$
C) $x ^ { 2 } + y ^ { 2 } - 4 x + 6 y + 4 = 0$
D) $x ^ { 2 } + y ^ { 2 } + 4 x - 6 y + 4 = 0$

Question

Quizplus · Accepted Answer

The center of the circle is $(2, -3)$, and the radius is the distance from the center to the point $(5, -3)$, which is 3. The equation of the circle is $(x - 2)^2 + (y + 3)^2 = 9$. Expanding this gives $x^2 - 4x + 4 + y^2 + 6y + 9 = 9$, which simplifies to $x^2 + y^2 - 4x + 6y + 4 = 0$.

Find the General Form of the Equation of the The Circle