Question

How do you graph `(x+2)^2 + (y+3)^2 = 4`?

Answer 1

You determine the centre, vertices, and endpoints. Then you plot the graph.

Explanation:

`(x+2)^2 + (y+3)^2 = 4`

This is the standard form for the equation of a circle with centre at (`-2,-3`) and radius `sqrt4 = 2`.

This means that, to find the vertices, you go 2 units up from the centre and 2 units down.

Thus, the vertices are at (`-2,-1`) and (`-2,-5`).

To find the endpoints, you go 2 units left of the centre and 2 to the right.

Thus, the endpoints are at (`-4,-3`) and (`0,-3`).

Plot the centre , the vertices, and the endpoints on a graph.

Now draw a smooth circle through the four outer points.

And you have your graph.