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Question 626812: Find a general form of an equation of the line that has y-intercept 3/2 and passes through the center of the circle with endpoints of a diameter A(4, -3) and B(-2, 7).
*I tried to solve this by doing point-slope form since I had a point or two, and the slope already given to me. When I did that I ended up with 2x+3y=17 somehow, which I know isn't right. Then I tried finding the midpoint, and calculating slope to put into point slope form, which also didn't work. I know that the answer is x-2y=-3, but I would like to know the steps and approach to get to the right answer. Thank you!
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find a general form of an equation of the line that has y-intercept 3/2 and passes through the center of the circle with endpoints of a diameter A(4, -3) and B(-2, 7).
*I tried to solve this by doing point-slope form since I had a point or two, and the slope already given to me. When I did that I ended up with 2x+3y=17 somehow, which I know isn't right. Then I tried finding the midpoint, and calculating slope to put into point slope form, which also didn't work. I know that the answer is x-2y=-3, but I would like to know the steps and approach to get to the right answer.
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Find the center of the circle.
C is (1,2)
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Find a general form of an equation of the line that has y-intercept 3/2 and passes through the center of the circle with endpoints of a diameter A(4,-3) and B(-2,7).
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Find the slope, m
m = diffy/diffx = (1.5 - 2)/(0 - 1)
m = 1/2
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y = mx + b
2 = (1/2)1 + b
b = 3/2
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--> y = (1/2)x + 3/2
x - 2y = -3
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