Write the standard form of the equation of the circle with the given characteristics.
Center:(3, 1); Radius: 7

A) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49$
B) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 7$
C) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + 7 = 0$
D) $x ^ { 2 } + y ^ { 2 } = 0$
E) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - 49 = 0$

Question

Write the standard form of the equation of the circle with the given characteristics. 
Center:(3, 1); Radius: 7
 
A) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49$
B) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 7$
C) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } + 7 = 0$
D) $x ^ { 2 } + y ^ { 2 } = 0$
E) $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } - 49 = 0$

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. Given the center $(3, 1)$ and radius $7$, the equation becomes $(x - 3)^2 + (y - 1)^2 = 7^2$, which simplifies to $(x - 3)^2 + (y - 1)^2 = 49$.

Write the Standard Form of the Equation of the Circle (x−3)2+(y−1)2=49( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49(x−3)2+(y−1)2=49

Write the Standard Form of the Equation of the Circle $( x - 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 49$