Equation of a circle with radius r, and center at (h, k). \((x - h)^2 + (y - k)^2 = r^2\)
Start by finding two things: 1. What is the radius of the circle? 2. What are the coordinates of the center of the circle?
@biddyB Are you there?
Sorry I was actually wrong! mathstudent55 is right. Sorry for the confusion!
Ok, whew, I was really confused for a second. Thats ok, I get it now, thanks
How do I find the radius?
First, find the center.
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.
Now that you know where the center is, the radius is the distance from the center point to any point on the circle.
It's easier if you measure along a horizontal or a vertical line.
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.
\((x - h)^2 + (y - k)^2 = r^2\) \((x - 0)^2 + (y - 0)^2 = 3^2\) You see the substitutions of 0 for h, 0 for k, and 3 for r?
Now we just simplify to: \(\large x^2 + y^2 = 9\) That is the answer.
Thank you! that was really well explained, I get it
For this one r=4? that seems too simple @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.
Correct. Now you let h = 3, k = 5, and r = 4, and you substitute these values in the equation of a circle.
(x-3)^2 +(y-5)^2=4^2 ?
That's it, it doesn't get simplified any more?