Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points. $( 0,0 ) , ( 0,12 ) , ( 6,6 )$
A) $x ^ { 2 } - y ^ { 2 } + 12 y = 0$
B) $x ^ { 2 } - y ^ { 2 } - 12 y = 0$
C) $- x ^ { 2 } + y ^ { 2 } - 12 y = 0$
D) $x ^ { 2 } + y ^ { 2 } - 12 y = 0$
E) $x ^ { 2 } + y ^ { 2 } + 12 y = 0$

Question

Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points.   $( 0,0 ) , ( 0,12 ) , ( 6,6 )$  
A)  $x ^ { 2 } - y ^ { 2 } + 12 y = 0$
B)  $x ^ { 2 } - y ^ { 2 } - 12 y = 0$
C)  $- x ^ { 2 } + y ^ { 2 } - 12 y = 0$
D) $x ^ { 2 } + y ^ { 2 } - 12 y = 0$
E)  $x ^ { 2 } + y ^ { 2 } + 12 y = 0$

Quizplus · Accepted Answer

To find the equation of the circle, we substitute the given points into the general equation $x^2 + y^2 + Dx + Ey + F = 0$ and solve for $D$, $E$, and $F$.1. Substituting $(0,0)$: $0 + 0 + 0 + 0 + F = 0$, so $F = 0$.2. Substituting $(0,12)$: $0 + 144 + 0 + 12E + 0 = 0$, so $12E = -144$, hence $E = -12$.3. Substituting $(6,6)$: $36 + 36 + 6D + 6E + 0 = 0$, with $E = -12$, we get $72 + 6D - 72 = 0$, so $6D = 0$, hence $D = 0$.Therefore, the equation of the circle is $x^2 + y^2 - 12y = 0$.

Find the Equation of the Circle x2+y2+Dx+Ey+F=0x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0x2+y2+Dx+Ey+F=0

Find the Equation of the Circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$