Write the standard form of the equation of the circle with center (3,-2)and solution point (-2,3). ?
A) $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
B) $( x - 3 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = \sqrt { 50 }$
C) $( x - 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$
D) $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = \sqrt { 50 }$
E) $( x - 3 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 50$

Question

Quizplus · Accepted Answer

The standard form of the equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. The center is given as $(3, -2)$, so $h = 3$ and $k = -2$, which matches the form in option E. To find $r^2$, calculate the distance between the center $(3, -2)$ and the solution point $(-2, 3)$ using the distance formula: $r^2 = (3 - (-2))^2 + (-2 - 3)^2 = 5^2 + (-5)^2 = 25 + 25 = 50$.

Write the Standard Form of the Equation of the Circle (x+3)2+(y−2)2=50( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50(x+3)2+(y−2)2=50

Write the Standard Form of the Equation of the Circle $( x + 3 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 50$