Problem 10
Answer: (x+5)^2+(y-3)^2=25
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Work Shown:
All we're doing really is replacing the original 'y' with 'y-3' to shift the center up 3 units. This shifts every point on the circle the same as well.
This new circle has center (-5,3) and radius 5. The old center was (-5,0). The radius stayed the same.
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Problem 11
Answer: (x-8)^2+(y-15)^2 = 9
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Work Shown:
x^2+y^2-16x-30y+280 = 0
(x^2-16x)+(y^2-30y)+280 = 0
(x^2-16x+64)-64+(y^2-30y+225)-225+280 = 0
(x-8)^2+(y-15)^2-9 = 0
(x-8)^2+(y-15)^2 = 9
This circle has center (8,15) and radius 3.
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Problem 12
Answer: (x+6)^2+(y-11)^2 = 20
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Work Shown:
x^2+y^2+12x-22y+137 = 0
(x^2+12x)+(y^2-22y)+137 = 0
(x^2+12x+36)-36+(y^2-22y+121)-121+137 = 0
(x+6)^2+(y-11)^2-20 = 0
(x+6)^2+(y-11)^2 = 20
This circle has center (-6,11) and radius sqrt(20) = 2*sqrt(5).
