Question 203606: please help me to: find the equation of the line segment, which is the shortest chord of the circle x^2+y^2=9 and passes through the poin (1,2).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the equation of the line segment, which is the shortest chord of the circle x^2+y^2=9 and passes through the poin (1,2).
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All the points on the circle have the form (x,sqrt(9-x^2))
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You want the distance from (1,2)to a point on the line to be a minimum.
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distance = sqrt[(1-x)^2 + (2-sqrt(9-x^2))^2]
D = sqrt[1 - 2x + x^2 + 4 - 4sqrt(9-x^2) + (9-x^2)]
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D = sqrt[14 -2x + 4sqrt(9-x^2)]
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Find the derivative of D:
Set it equal to zero and solve for "x":
Find the corresponding y-value on the circle.
Use that point and the point (1,2) to find the equation of the line you want.
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Cheers,
Stan H.
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