Question

Gilbert drew the incorrect graph shown below to represent the circle (x +2)2 + (y −1)2 = 9
Which statement explains why Gilbert’s graph is incorrect?

The radius of the circle should be 2 instead of 9.

The center of the circle should be (2, -1) instead of (-2, 1).

The radius of the circle should be 3 instead of 9.

The center of the circle should be (-1, 9) instead of (-2, 1).

Answer 1

Do you know how to find the center and radius from the circle equation? You can compare this to what is on the graph.

Answer 2

find the square root i think

Answer 3

Hmm... the general equation looks like this:
\( (x-h)^2 + (y-k)^2 = r^2 \)
The parallels we can see between this general form and the given equation help identify the properties of the graph, like what's in the place for the radius and the (h,k) values.

Answer 4

So is it D ?

Answer 5

What I meant was, it's in this general form, so we can find the center, (h,k), and the radius, r, just by looking at the components.
\((x \color{red}{+2})^2 + (y \color{green}{−1})^2 = \color{blue}9\)
\((x \color{red}{- h})^2 + (y \color{green}{-k})^2 = \color{blue}{r^2} \)
-h = 2, so h = -2
-k = -1, so k = 1
r^2 = 9, so r = 3

That makes sense?

Answer 6

Sort of so the answer is actually C ?

Answer 7

Yes. :)

We can see from the graph that he used radius 9, which is not the radius of the given circle that we found. These sorts of comparisons are what you want to look into when identifying the errors: what are the properties of the correct version, and do they compare with the erroneous version.

Answer 8

Oh , thanks so much !

Answer 9

You're welcome. :)