SOLUTION: Find the equation of the circle with center (-4,-5) and tangent to the line 2x+7y-10=0?

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Question 936969: Find the equation of the circle with center (-4,-5) and tangent to the line 2x+7y-10=0?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
If it's tangent to the line, then a line from the center point to the intersection point is perpendicular to the tangent line.
2x%2B7y=10
7y=-2x%2B10
y=-%282%2F7%29x%2B10%2F7
The perpendicular line would have a slope of
m%28-2%2F7%29=-1
m=7%2F2 Slope of the perpendicular line
since perpendicular lines have slopes that are negative reciprocals.
Using the point,
y-%28-5%29=%287%2F2%29%28x-%28-4%29%29
y%2B5=%287%2F2%29%28x%2B4%29
y%2B5=%287%2F2%29x%2B14
y=%287%2F2%29x%2B9 Equation of the perpendicular line
Find the intersection point of the two lines.
%287%2F2%29x%2B9=-%282%2F7%29x%2B10%2F7
Multiply both sides by 14.
49x%2B126=-4x%2B20
53x=-106
x=-2
y=%287%2F2%29%28-2%29%2B9
y=-7%2B9
y=2
The distance from (-4,-5) to (-2,2) is the radius of the circle.
R%5E2=%28-2-%28-4%29%29%5E2%2B%282-%28-5%29%29%5E2
R%5E2=%28-2%2B4%29%5E2%2B%282%2B5%29%5E2
R%5E2=2%5E2%2B7%5E2
R%5E2=4%2B49
R%5E2=53
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highlight_green%28%28x%2B4%29%5E2%2B%28y%2B5%29%5E2=53%29
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