1. Writing Equations by Completing the Square Or Using the Distance Formula

2.   Let’s start by reviewing the equation of a circle:  (x – h) 2 + (y – k) 2 = r 2  Write the equation of the circle with a center at (5, -6) and a radius of 7.  (x – 5) 2 + (y + 6) 2 = 49  Find the center and radius of the circle give the equation.  (x – 5) 2 + (y - 3) 2 = 4  Center (5, 3) r = 2 Circles

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4.   Write the equation of the circle in standard form.  x 2 – 8x + y 2 + 20y + 107 = 0  (x 2 – 8x + ___) + (y 2 + 20y + __) = - 107 +___ + ___  (x 2 – 8x + 16) + (y 2 + 20y + 100) = - 107+ 16 + 100  (x – 4) 2 + (y + 10) 2 = 9  Center (4, - 10) r = 3 Circles  Group the x’s and the y’s and move the constant over.  Don’t forget to put in the blanks.  Find both of the c’s to fill in the blanks.  Factor the two equations and combine the numbers on the right.  Now you have your equation!!

5.   I know that seemed like a lot, so….  …try again!  Transform the equation to standard form.  x 2 + y 2 + 4x – 6y – 12 = 0  (x 2 + 4x + ___) + (y 2 - 6y + ___) = 12 + ___ +___  (x 2 + 4x + 4) + (y 2 - 6y + 9) = 12 + 4 + 9  (x + 2) 2 + (y – 3) 2 = 25  Center (-2, 3) r = 5 Circles

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9.   Try a couple, they are pretty easy.  Centered at (7, - 8) and passing through (10, -4)  (x – 7) 2 + (y + 8) 2 = 25  Centered at (5, 6) and passing through (-1, -2)  (x – 5) 2 + (y – 6) 2 = 100  Centered at (-4, -9) and passing through (1, 0)  (x + 4) 2 + (y + 9) 2 = 106 Circles