How do you write an equation of a circle in standard form?

Question

bloomlocke367 · Answer

@iGreen

igreen · Answer

This is the standard form of a circle:

$(x−h)^2+(y−k)^2=r^2$

Do you have a specific equation?

bloomlocke367 · Answer

ohhhh, no I have a graph and I have to write the equation from the graph

igreen · Answer

Oh, okay

igreen · Answer

Post the graph

bloomlocke367 · Answer

okay.

igreen · Answer

$(h, k)$ is the center of the circle

bloomlocke367 · Answer

attachment

bloomlocke367 · Answer

okay.

igreen · Answer

Okay, find the center of the circle, what is it?

bloomlocke367 · Answer

(3,5)?

igreen · Answer

Yep!

bloomlocke367 · Answer

don't I have to use the pathagorean theorem to find the radius?

bloomlocke367 · Answer

and I so spelled that incorrectly XD

igreen · Answer

So let's plug it in our equation.

$(x−h)^2+(y−k)^2=r^2$

$(h, k)$ is the center:

$(x−3)^2+(y−5)^2=r^2$

Now we can find the answer

igreen · Answer

Click on a different question and come back here, and those question marks will disappear

igreen · Answer

Which option do you think is correct? We can already find the answer from here.

bloomlocke367 · Answer

okay, you're right, because all of the r^2 is the same. but how would I find that. I think I remember seeing something about using the pythagorean theorem for the radius of a circle

igreen · Answer

No..

igreen · Answer

We can just find the radius by looking at the circle

igreen · Answer

Start at the center and count the number of units you need to take to reach the end of the circle

igreen · Answer

I get 8 units, so we plug in 8 for 'r':

So let's plug it in our equation.

$(x-3)^2+(y-5)^2=8^2$

Simplify $8^2$:

$(x-3)^2+(y-5)^2=64$

bloomlocke367 · Answer

okay...

bloomlocke367 · Answer

but what about that?...

bloomlocke367 · Answer

@iGreen that's what my teacher showed me...

bloomlocke367 · Answer

@iGreen