SOLUTION: Write the equation of a circle that passes through the points A(4;0) , B(0;2) and whose center belongs to the line of equation y+2x=0

Algebra ->  Graphs -> SOLUTION: Write the equation of a circle that passes through the points A(4;0) , B(0;2) and whose center belongs to the line of equation y+2x=0      Log On


   

Question 700101: Write the equation of a circle that passes through the points A(4;0) , B(0;2) and whose center belongs to the line of equation y+2x=0
Answer by Alan3354(69443) About Me  (Show Source):
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Write the equation of a circle that passes through the points A(4;0) , B(0;2) and whose center belongs to the line of equation y+2x=0
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Find the center. The center is equidistant from the 2 points and on the line.
--> The center will be on the line that's the perpendicular bisector of the line joining the 2 points.
The slope of lines thru the 2 points = -1/2 --> perpendicular lines have a slope of +2.
The midpoint of A & B is (2,1)
Using y = mx+b and (2,1) --> y = 2x - 3 is the perp. bisecting line.
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The center is the intersection of y = 2x-3 and y+2x = 0
--> (3/4,-3/2)
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The radius is the distance from the center to either A or B
r%5E2+=+3.25%5E2+%2B+1.5%5E2+=+12.8125
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the circle is %28x+-+3%2F4%29%5E2+%2B+%28y+%2B+3%2F2%29%5E2+=+12.8125
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PS Use commas for points, eg, (4,0) and (0,2)