Page 99 - Calc for the Clueless

The distance formula:

2
2
Squaring, we get (x - h) + (y- k) = r 2
Example 11—

Find the radius and center if (x - 4) + (y + ½) = 11. r = 11 , center (4,-½).
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1/2
2
Example 12—
2
2
Find the center and radius of the circle 2x + 2y + 8x -16y+6=0.
In order to do this, we have to complete the square, something we have not done since the derivation of the
quadratic formula.

2
Divide by the coefficient of x .

Group the x terms and y terms; get the constant to the other side.

Take half of 4, square it, add it to both sides, and take half of -8, square it, add it to both sides.

Factor into perfect squares (that was the idea) and add the terms on the right.

The center is (-2,4), r = 17 .
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