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

Answer:

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

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