How do you graph $x^{2} + {(y + 2)}^{2} = 9$ $x^2 + (y + 2)^2 = 9$ ?

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Answer 1 · 2015-07-08T16:19:55

You convert the equation to standard form, determine the centre, vertices, and endpoints. Then you plot the graph.

$x^{2} + {(y + 2)}^{2} = 9$ $x^2 + (y+2)^2 = 9$

This is almost the standard form for the equation of a circle.

Let's modify it to read

${(x - 0)}^{2} + {(y + 2)}^{2} = 9$ $(x-0)^2 + (y+2)^2 = 9$

Now we see that it is a circle with centre at ( $0, - 2$ $0,-2$ ) and radius $\sqrt{9} = 3$ $sqrt9 = 3$ .

This means that, to find the vertices, you go 3 units up from the centre and 3 units down.

Thus, the vertices are at ( $0, 1$ $0,1$ ) and ( $0, - 5$ $0,-5$ ).

To find the endpoints, you go 3 units left of the centre and 3 to the right.

Thus, the endpoints are at ( $- 3, - 2$ $-3,-2$ ) and ( $3, - 2$ $3,-2$ ).

Plot these points on a graph.

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Now draw a smooth circle through these four points.

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And you have your graph.

How do you graph x2+(y+2)2=9x^2 + (y + 2)^2 = 9?