Write the equation for the shape described.
-The circle with center (19, 17), containing the origin
A) $( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 650$
B) $( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 25$
C) $( x - 17 ) ^ { 2 } + ( y - 19 ) ^ { 2 } = 650$
D) $( x - 17 ) ^ { 2 } + ( y - 19 ) ^ { 2 } = 25$

Question

Write the equation for the shape described.
-The circle with center (19, 17), containing the origin 
A) $( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 650$
B) $( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 25$
C) $( x - 17 ) ^ { 2 } + ( y - 19 ) ^ { 2 } = 650$
D) $( x - 17 ) ^ { 2 } + ( y - 19 ) ^ { 2 } = 25$

Quizplus · Accepted Answer

The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. The distance from the center $(19, 17)$ to the origin $(0, 0)$ is $\sqrt{(19-0)^2 + (17-0)^2} = \sqrt{361 + 289} = \sqrt{650}$, so the radius squared is $650$. Therefore, the correct equation is $(x - 19)^2 + (y - 17)^2 = 650$.

Write the Equation for the Shape Described (x−19)2+(y−17)2=650( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 650(x−19)2+(y−17)2=650

Write the Equation for the Shape Described $( x - 19 ) ^ { 2 } + ( y - 17 ) ^ { 2 } = 650$