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

1 Answer
Aug 7, 2015

Answer:

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.

Graph1

Now draw a smooth circle through the four outer points.

Graph2

And you have your graph.