<PRE><B>Question 979454</B>
Find the equation of a circle that passes through (2,2) and tangent to the lines x=1 and x=6.
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The center has to be on the line midway between x=1 and x=6, which is
x = 3.5
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The radius is the distance from x=3.5 to the tangent lines, r = 2.5
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The center is on the line x = 3.5 and is 2.5 units from the point (2,2).
The circle with its center at (2,2) and r=2.5 is
{{{(x-2)^2 + (y-2)^2 = 2.5^2}}}
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Find the intersection of {{{(x-2)^2 + (y-2)^2 = 2.5^2}}} and x=3.5
Sub 3.5 for x and solve for y:
{{{(3.5-2)^2 + (y-2)^2 = 2.5^2}}}
{{{2.25 + y^2 - 4y + 4 = 6.25}}}
{{{y^2 - 4y = 0}}}
y = 0, y = 4
The 2 centers are (3.5,0) and (3.5,4)
Can you finish it?

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