Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)
A) $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 13$
B) $( x - 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 1$
C) $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 13$
D) $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$
E) $( x + 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 17$

Question

Quizplus · Accepted Answer

The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Given the center $(-5, -4)$, the equation starts as $(x + 5)^2 + (y + 4)^2$. To find $r^2$, calculate the distance between the center and the solution point $(-3, -7)$ using the distance formula: $r^2 = (-3 + 5)^2 + (-7 + 4)^2 = 2^2 + (-3)^2 = 4 + 9 = 13$.

Write the Standard Form of the Equation of the Circle (x+5)2+(y+4)2=13( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 13(x+5)2+(y+4)2=13

Write the Standard Form of the Equation of the Circle $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 13$