Write the standard form of the equation of the circle with the given characteristics.
center: $( - 1,4 )$; radius: 3
A) $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$
B) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$
C) $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$
D) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$
E) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$

Question

Write the standard form of the equation of the circle with the given characteristics. 
center: $( - 1,4 )$; radius: 3
A) $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 9$
B) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$
C) $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 9$
D) $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$
E) $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$

Quizplus · Accepted Answer

The standard form of the equation of a circle with center $(h,k)$ and radius $\text{r}$ is $$(x-h)^2+(y-k)^2=\text{r}^2.$$ Substituting $(-1,4)$ for $(h,k)$ and 3 for $\text{r}$ gives us $(x+1)^2+(y-4)^2=9$, which is the equation in standard form. Therefore, the best choice is (C).

Write the Standard Form of the Equation of the Circle (−1,4)( - 1,4 )(−1,4)

Write the Standard Form of the Equation of the Circle $( - 1,4 )$