SOLUTION: i don't really understand how to do this problem. if you could please explain how to do it asap. thank you. Write the equation of the circle in center and radius form. State the

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Question 264228: i don't really understand how to do this problem. if you could please explain how to do it asap. thank you.
Write the equation of the circle in center and radius form. State the center and the radius:
x^2+y^2-2x+8y-10=0
Found 2 solutions by stanbon, dabanfield:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Write the equation of the circle in center and radius form. State the center and the radius:
x^2+y^2-2x+8y-10=0
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Complete the square on the x-terms and on the y-terms.
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x^2 - 2x + ? + y^2 + 8y + ? = -10 + ?
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x^2-2x+1 + y^2+8y+16 = -10+1+16
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(x-1)^2 + (y+4)^2 = 7
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Center: (1,-4)
Radius: sqrt(7)
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Cheers,
Stan H.

Answer by dabanfield(803) (Show Source):
You can put this solution on YOUR website!
i don't really understand how to do this problem. if you could please explain how to do it asap. thank you.
Write the equation of the circle in center and radius form. State the center and the radius:
x^2+y^2-2x+8y-10=0
We need to rewrite the above in the form:
(x-a)^2 + (y-b)^2 = r^2
The above is the equation of a circle with center at point (a,b) and radius = r.
1.) x^2 + y^2 -2x + 8y - 10 = 0
2.) (x^2 - 2x) + (y^2 + 8y) = 10
Let's "complete the square" on each of the two groups of terms on the left. Note that when we add constants to the left side of the equation we also must add the same constants to the right side:
3.) (x^2 - 2x - 1) + (y^2 + 8y + 16) = 10 - 1 + 16
4.) (x - 1)^2 + (y + 4)^2 = 25
This is the equation of a cirlc with center at (1,-4) and radius = 5.