Question 187485: I have a geometry question that is on my worksheet for my homework. My worksheet is labeled Distance in Coordinate Geometry. My question is Given circle O with O(3,-4) and radius 5, find 12 points on the circle with integer coordinates.
I am stuck. I have been taught the formula for finding the equation of a circle which was tuaght to me like this:
EXAMPLE: If the radius of a circle is 16 and the coordinates of the centerpoint are (3,4), then what is the equation?
First, you put the x coordinate of the centerpoint into the first set of parantheses adn the y into the second set of parantheses. It should look like this  .
I hope that this is clear enough. I get stuck here trying to figure out the coordinates of the points on the circle. I think that one of them is (8,-4). Are you suposed to just continue choosing random points to find the points, or is there an easier way? Please help, and thank you so much!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! My question is Given circle O with O(3,-4) and radius 5, find 12 points on the circle with integer coordinates.
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Equation:
(x-3)^2 + (y+4)^2 = 25
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I think you will see the answer if you plot the center at (3,-4)
Since the radius is "5" draw a radius to (0,0).
Do you see the 3-4-5 right triangle with vertices at (0,0),
(3,-4) and (0,-4)?
If you do, plot the point (0,-8); it also forms a 3-4-5 rt.
triangle with vertices (0,-4), (3,-4),(0.-8)
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Go up 5 from (3,-4) to (3,1).
Go down5 from (3,-4) to (3,-9)
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So far you have four solution points with integer values.
Can you find the other 8?
Consider the symmetry a circle has.
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Cheers,
Stan H.
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