Question 995162
Help me find the equation of a circle passing through points (6,0) and (24,0) and is a tangent to the y-axis
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Label the points A(6,0) and B(24,0)
The center of the circle, point C, is on the perpendicular bisector of AB, which is x = 15
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Tangent to the y-axis makes the radius 15.
The distance from A and B to the center is also 15.
{{{AC = sqrt(diffy^2 + diffx^2) = sqrt((y-0)^2 + 9^2) = 15}}}
{{{y^2 + 81 = 225}}}
y = 12
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Center at (15,12) and (15,-12) (there are 2 circles)
(15,12) --> {{{(x-15)^2 + (y-12)^2 = 15^2}}}
(15,-12) --> {{{(x-15)^2 + (y+12)^2 = 15^2}}}