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What is the equation of the circle that has a diameter joining the points (3, 6) and...

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lxsptter | Student, Undergraduate | Valedictorian

Posted May 29, 2013 at 6:06 PM via web

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What is the equation of the circle that has a diameter joining the points (3, 6) and (8, 10)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 29, 2013 at 6:15 PM (Answer #1)

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The circle has a diameter that joins the points (3, 6) and (8, 10). The center of the circle is the point that lies between (3, 6) and (8, 10). This is ((3+8)/2, (6+10)/2) = (11/2, 8)

The radius of the circle is half the distance between the given points.

r = (1/2)*sqrt((8 - 3)^2 + (10 - 6)^2)

The equation of a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

=> (x - 11/2)^2 + (y - 8)^2 = 41/4

=> 4x^2 + 121 - 44x + 4y^2 + 256 - 64y = 41

=> 4x^2 + 4y^2 - 44x - 64y + 336 = 0

The equation of the circle is 4x^2 + 4y^2 - 44x - 64y + 336 = 0

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aruv | High School Teacher | Valedictorian

Posted May 30, 2013 at 7:15 AM (Answer #2)

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End points of diameter are (3,6) and (8,10).

Since angle in semi circle is right angle.Let (x,y) be any point in semicircle.

Find slope of lines joing end points of diameter.

`m_1=(y-6)/(x-3)`

`m_2=(y-10)/(x-8)`

`m_1 m_2={(y-6)/(x-3)}{(y-10)/(x-8)}=-1`

Equation of circle is

`(x-3)(x-8)+(y-6)(y-10)=0`

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