Find the equation of the circle $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$ that passes through the points $( 3,4 ) , ( 0,1 ) , ( 6,1 )$ .
A) $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 1 = 0$
B) $x ^ { 2 } + y ^ { 2 } - 3 x - y + 1 = 0$
C) $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y + 19 = 0$
D) $x ^ { 2 } + y ^ { 2 } - 6 x - 2 y - 9 = 0$
E) $x ^ { 2 } + y ^ { 2 } - 3 x - y - 9 = 0$

Question

Quizplus · Accepted Answer

To find the equation of the circle, substitute the given points into the general equation $x^2 + y^2 + Dx + Ey + F = 0$ and solve for $D$, $E$, and $F$. Substituting the points $(3,4)$, $(0,1)$, and $(6,1)$ gives a system of equations. Solving this system yields $D = -6$, $E = -2$, and $F = 1$, resulting in the equation $x^2 + y^2 - 6x - 2y + 1 = 0$.

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 $x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$