Question

What is the equation of the circle shown?785432.А1-B-8-5-4-3-2-1 02.4-1-2-3-4-5(x2 + (y)2 =IIWord Bank:10 -2 5 + 2 - 1+ 1 25Blank 1:Blank 2:Blank 3:

Answer 1

Consider that the equation of a circle with center (h,k) and radius 'r' units, is given by,

$(x-h)^2-(y-k)^2=r^2$

Observe the given diagram carefully.

The center of the circle lies at (-2,1),

$(h,k)=(-2,1)$

The radius of the circle is the distance of any point on the circle from the center. Since the point (3,0) lies on the circle, the radius is calculated as,

$r=3-(-2)=3+2=5$

Substitute the values in the standard equation of circle,

$\begin{gathered} (x-(-2))^2-(y-1)^2=5^2 \\ (x+2)^2-(y-1)^2=25 \end{gathered}$

Thus, the equation of the given circle is,

$(x+2)^2-(y-1)^2=25$