Question

What is the equation of the circle shown in the graph

Answer 1

The general equation for a circle is:
$(x-h)^2 + (y-k)^2 = r^2$

where (h,k) is center of circle
r = radius

For this example, from the graph you see the center is at (0,-3) and radius is 2.
h  = 0, k = -3, r = 2

Sub into general equation:
$(x-0)^2 + (y-(-3))^2 = 2^2 \\ \\ x^2 +(y+3)^2 = 4$

Answer 2

The equation of the circle will be x² + (y + 3)² = 4. Then the correct option is C.

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The center of the circle is at (0, -3) and the radius of the circle is 2 units. Then the equation of the circle will be

(x - 0)² + (y - (-3))² = 2²

         x² + (y + 3)² = 4

Then the correct option is C.

Learn more about the equation of a circle here:

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