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

Question

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

Quizplus · Accepted Answer

Substituting the given points into the general equation of the circle $x^2 + y^2 + Dx + Ey + F = 0$, we get three equations: 1. Substituting (0,0) gives $0 + 0 + 0 + 0 + F = 0$, so $F = 0$.2. Substituting (0,-3) gives $0 + 9 + 0 - 3E + 0 = 0$, so $E = 3$.3. Substituting (4,0) gives $16 + 0 + 4D + 0 + 0 = 0$, so $D = -4$.Thus, the equation of the circle is $x^2 + y^2 - 4x + 3y = 0$.

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