Question 1185888
find the equation of the circle that passes through the point (9 7) and is tangent to both x and y axis and the line 3x-4y=24
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Ignore the line 3x-4y=24.
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The point (9,7) and tangent to the axes defines the circle.
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Thru a point in Q1 and tangent to both axes --> the center is on the line y = x
With center at (h,k):
{{{(x-h)^2 + (y-k)^2 = r^2}}}
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The distance from (9,7) to the center = the distance from (x,0) to the center.
{{{(9-x)^2 + (7-x)^2 = x^2}}}
{{{130 - 32x + 2x^2 = x^2}}}
{{{x^2 - 32x + 130 = 0}}}
r = x
---> {{{(x - 4.775)^2 + (y - 4.775)^2 = 4.775^2}}}
Some lines seem to get lost.
There is no circle that meets all the constraints.
You can eliminate the point and find a circle tangent to the axes and the given line, but then it won't pass thru (9,7).