Question 184708: HELP PLEASE
x^+10x+y^-6y+9=0 represents a circle. find radius and centre.
also find any point an circle that intersects line y=-x+3
any assistance would be greatly appreciated.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! x^2+10x+y^2-6y+9=0 represents a circle. find radius and centre.
also find any point an circle that intersects line y=-x+3
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Complete the square on the x-terms and on the y-terms, as follows:
x^2 + 10x + ? + y^2 -6y + ? = -9 + ?+?
x^2 + 10x + 25 + y^2 - 6y + 9 = -9 + 25 + 9
(x+5)^2 + (y-3)^2 = 25
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center is (-5,3)
radius = sqrt(25) = 5
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Find any point on the circle that intersects line y=-x+3
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Substitute for "y" in the circle equation to solve for "x".
(x+5)^2 + (-x+3-3)^2 = 25
x^2 + 10x + 25 + x^2 = 25
2x^2 + 10x = 0
2x(x+5) = 0
x = 0 or x = -5
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Usiing y = -x+3, for the y-values that correspond to x = 0 and to x=-5:
If x=0, y = 3
If x = -5, y = 8
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Intersection points are (0,3) and (-5,8)
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Cheers,
Stan H.
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