Find the equation of the circle
$$x ^ { 2 } + y ^ { 2 } + D x + E y + F = 0$$
that passes through the points $( 1,9 ) , ( - 4,4 ) , ( 6,4 )$.
A) $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 8 = 0$
B) $x ^ { 2 } + y ^ { 2 } - x - 4 y - 8 = 0$
C) $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y + 42 = 0$
D) $x ^ { 2 } + y ^ { 2 } - 2 x - 8 y - 25 = 0$
E) $x ^ { 2 } + y ^ { 2 } - x - 4 y - 25 = 0$

Question

Quizplus · Accepted Answer

The equation of the circle is in the form $x^2 + y^2 + Dx + Ey + F = 0$. Substituting the given points into the equation, we get the following system of equations:$1^2 + 9^2 + D(1) + E(9) + F = 0$$(-4)^2 + 4^2 + D(-4) + E(4) + F = 0$$6^2 + 4^2 + D(6) + E(4) + F = 0$Solving this system of equations, we get the values of D, E, and F as follows:$D = -2$$E = -8$$F = -8$Therefore, the equation of the circle is $x^2 + y^2 - 2x - 8y - 8 = 0$.

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