anonymous
  • anonymous
What is the equation of the following graph?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
mathstudent55
  • mathstudent55
Equation of a circle with radius r, and center at (h, k). \((x - h)^2 + (y - k)^2 = r^2\)
mathstudent55
  • mathstudent55
Start by finding two things: 1. What is the radius of the circle? 2. What are the coordinates of the center of the circle?

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mathstudent55
  • mathstudent55
@biddyB Are you there?
anonymous
  • anonymous
Sorry I was actually wrong! mathstudent55 is right. Sorry for the confusion!
anonymous
  • anonymous
Ok, whew, I was really confused for a second. Thats ok, I get it now, thanks
anonymous
  • anonymous
How do I find the radius?
mathstudent55
  • mathstudent55
First, find the center.
anonymous
  • anonymous
0?
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
I think you got the right idea, but the center is actually (0, 0) since it's a point. It needs to have an x-coordinate and a y-coordinate.
mathstudent55
  • mathstudent55
Now that you know where the center is, the radius is the distance from the center point to any point on the circle.
mathstudent55
  • mathstudent55
It's easier if you measure along a horizontal or a vertical line.
mathstudent55
  • mathstudent55
|dw:1438645313174:dw|
anonymous
  • anonymous
3?
mathstudent55
  • mathstudent55
Correct. The radius is 3. That means r = 3 The center of the circle is (0, 0). That means h = 0, and k = 0. Now we use these values in the equation above.
mathstudent55
  • mathstudent55
\((x - h)^2 + (y - k)^2 = r^2\) \((x - 0)^2 + (y - 0)^2 = 3^2\) You see the substitutions of 0 for h, 0 for k, and 3 for r?
mathstudent55
  • mathstudent55
Now we just simplify to: \(\large x^2 + y^2 = 9\) That is the answer.
anonymous
  • anonymous
Thank you! that was really well explained, I get it
anonymous
  • anonymous
For this one r=4? that seems too simple @mathstudent55
anonymous
  • anonymous
mathstudent55
  • mathstudent55
Correct. For the second problem, r = 4. Now you need to coordinates of the center. What are they? Remember, you are looking for an ordered pair of the form (x, y) for the center.
anonymous
  • anonymous
(3,5)?
mathstudent55
  • mathstudent55
Correct. Now you let h = 3, k = 5, and r = 4, and you substitute these values in the equation of a circle.
anonymous
  • anonymous
(x-3)^2 +(y-5)^2=4^2 ?
mathstudent55
  • mathstudent55
Correct.
anonymous
  • anonymous
That's it, it doesn't get simplified any more?

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