Question 1185739: SOLVE USING GEOMETRIC CONSTRUCTION.
FIND THE EQUATION OF THE CIRCLE TANGET TO 3X+4Y-15=0 AT P1(1,3) AND PASSING THROUGH P2(6,3) AND P3(O,5)
SOLUTION AND CIRCLE TANGENT
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! SOLVE USING GEOMETRIC CONSTRUCTION.
FIND THE EQUATION OF THE CIRCLE TANGET TO 3X+4Y-15=0 AT P1(1,3) AND PASSING THROUGH P2(6,3) AND P3(O,5)
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Given 3 points: A(1,3), B(6,3) and C(0,5)
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Find the center of the circle;
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Step 1, find the perpendicular bisector of AB and of BC
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Midpoint of AB is (3.5,3)
Perp bisector is x = 3.5
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Midpoint of BC is (3,4)
Slope of BC is -1/3
Perp bisector is y = 3x - 5
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The center is the intersection of the 2 bisectors @ (3.5,5.5)
Radius is the distance from the center to any point = sqrt(12.5)
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The circle passes thru the 3 points, but is NOT tangent to the given line.
No such circle is possible.
An ellipse can be found to fit, or one of the 3 points eliminated for a circle.
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