SOLUTION: Write the equation of the circle havhng radius 13square root and tangent to the line 2x - 3y + 1 = 0 at (1,1)

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Question 1087452: Write the equation of the circle havhng radius 13square root and tangent to the line 2x - 3y + 1 = 0 at (1,1)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the line perpendicular to the tangent line through (1,1).
2x-3y%2B1=0
3y=2x%2B1
y=%282%2F3%29x%2B1%2F3
Perpendicular lines have slopes that are negative reciprocals,
%282%2F3%29m%5Bp%5D=-1
m%5Bp%5D=-3%2F2
y-1=-%283%2F2%29%28x-1%29
Find the center of the circle (x,y) using the radius from (1,1),
%28x-1%29%5E2%2B%28y-1%29%5E2=13
From above,
%28y-1%29%5E2=%28-%283%2F2%29%28x-1%29%29%5E2
%28y-1%29%5E2=%289%2F4%29%28x-1%29%5E2
Substituting,
%28x-1%29%5E2%2B%28y-1%29%5E2=13
%28x-1%29%5E2%2B%289%2F4%29%28x-1%29%5E2=13
%2813%2F4%29%28x-1%29%5E2=13
%28x-1%29%5E2=4
x-1=0+%2B-+2
x=-1 and x=3
Solving for y,
x=-1
y-1=-%283%2F2%29%28-1-1%29
y=4
Solving for y,
x=3
y-1=-%283%2F2%29%283-1%29
y=-2
So then the two circles are,
+%28x%2B1%29%5E2%2B%28y-4%29%5E2=13+
+%28x-3%29%5E2%2B%28y%2B2%29%5E2=13+
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