SOLUTION: Write the equation of the circle in standard form. Find the center , radius, intercepts, and graph the circle.
x^2 + y^2 - 8x + 14y = -29
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Question 660746: Write the equation of the circle in standard form. Find the center , radius, intercepts, and graph the circle.
x^2 + y^2 - 8x + 14y = -29
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the center , radius, intercepts, and graph the circle.
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Complete the square on the x and on the y terms:
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x^2 + y^2 - 8x + 14y = -29
(x^2 - 8x + 16)) + (y^2 + 14y + 49) = -29 + 16 + 49
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Factor:
(x-4)^2 + (y+7)^2 = 36
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Center: (4,-7)
Radius: sqrt(36) = 6
Intercepts:
x-intercepts: Let y = 0, then (x-4)^2 + 49 = 36 ;
then (x-4)^2 = -13
Therefore: no x-intercepts
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y-intercepts: let x = 0, then (-4)^2 + (y+7)^2 = 36,
then (y+7)^2 = 20
then y+7 = 2sqrt(5) or y+7 = -2sqrt(5)
y = -7+2sqrt(5) or y = -7-2sqrt(5)
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Cheers,
Stan H.
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