Use the given information about a circle to write an equation of the circle in standard form.
-The center is $( - 5 , - 4 )$ and another point on the circle is $( 1,4 )$
A) $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 100$
B) $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 10$
C) $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$
D) $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 10$

Question

Quizplus · Accepted Answer

The equation of a circle in standard form is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. Given the center $(-5, -4)$, the equation becomes $(x + 5)^2 + (y + 4)^2 = r^2$. To find $r^2$, calculate the distance between the center $(-5, -4)$ and the point on the circle $(1, 4)$ using the distance formula: $r^2 = (1 + 5)^2 + (4 + 4)^2 = 6^2 + 8^2 = 36 + 64 = 100$. Therefore, the correct equation is $(x + 5)^2 + (y + 4)^2 = 100$.

Use the Given Information About a Circle to Write an Equation