Question

identify the description that matches this equation. x² + (y - 3)² = 16 O A a circle with center (0,0) and radius 5 o B. a circle with center (0,3) and radius 4 0 C. a circle with center (0,-3) and radius 4 0 D. a circle with center (3,0) and radius 16

Answer 1

B. a circle with center (0,3) and radius 4

Step-by-step explanation:

Given the equation of the circle:

`x^2+(y-3)^2=16`

Compare it with the standard equation of a circle:

`(x-h)^2+(y-k)^2=r^2`

We see that:

`\begin{gathered} x^{}=x-h\implies h=0 \\ y-3=y-k\implies k=3 \\ r^2=16\implies r=4 \end{gathered}`

The centre of the circle is:

`(h,k)=(0,3)`

Therefore, the correct description is:

B. a circle with center (0,3) and radius 4