Question

Determine which of the following is the equation of the circle shown below

Answer 1

We need to first identify the center of the circle.

We see that the coordinate point of the center of the circle is (-1, -2).

The equation of a circle is given with the equation

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

where h is x, k is y, and r is the radius of the circle.

Therefore, we can plug in the coordinates first to find the h and k of the equation.

`\begin{gathered} (x-(-1))^2+(y-(-2))^2=r^2 \\ (x+1)^2+(y+2)^2=r^2_{} \end{gathered}`

Then, we need to determine r.

The circle intersects points (-6, -2) and (4, -2). We can simply subtract the x-coordinates from each other to find the diameter of the circle.

`-6-4=-10`

Finally, we know the radius is half of the diameter:

`(-10)/(2)=-5`

We can plug in the radius into the equation.

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

Therefore, our final equation is Choice D:

`(x+1)^2+(y+2)^2=25`