Finding the Radius and Center of a CircleDate: 06/19/2002 at 15:24:19 From: John Trikouros Subject: Radius and center of a circle I need help trying to figure out the center and the radius for the following equation: 2 2 X + 8X + Y - 6Y = 11 Thanks. Date: 06/19/2002 at 16:02:49 From: Doctor Jeremiah Subject: Re: Radius and center of a circle Hi John, You need to "complete the square" to get what you want. 2 2 X + 8X + Y - 6Y = 11 Now, since we can add things to one side as long as we add them to the other side, we can find a value that would turn (X^2 + 8X) into a factorable square and add it to the equation on both sides. Then we can do the same for (Y^2 - 6Y). When we do that we get: 2 2 X + 8X + 16 + Y - 6Y + 9 = 11 + 16 + 9 ^ ^ | | (8/2)^2 (6/2)^2 Now we just factor the terms into squares: 2 2 (X + 4) + (Y - 3) = 11 + 16 + 9 Now fix up the right side: 2 2 (X + 4) + (Y - 3) = 36 2 2 2 (X + 4) + (Y - 3) = 6 And you have an equation that shows the center and radius. Let me know if you still have questions. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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