Hi there!
Let's solve this problem step by step!
1. First we take a look at the circle in the graph.
The centre of the circle is located at the point (3, -2). The circle touches the vertical axis in the point (0, -2). We can therefore conclude that the radius of the circle is 3.
2. The general equation of a circle is as follows:
[tex](x - a) {}^{2} + (y - b) {}^{2} = r {}^{2} [/tex]
In this equation, the point (a, b) is the centre of the circle and r represents its radius.
3. Combine our knowledge from 1. and 2.
Let's substitute the centre and radius into our eqiation!
[tex](x - 3) {}^{2} + (y - - 2) {}^{2} = {3}^{2} [/tex]
Now we can square on the left side, and replace the two minus signs by a plus.
[tex](x - 3) {}^{2} + (y + 2) {}^{2} = 9[/tex]
Hence, the answer is D.
~ Hope this helps you!
