SOLUTION: Find the equation of the line tangent to a circle x2 + y2 = 13 at (3,-2).

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Question 856009: Find the equation of the line tangent to a circle x2 + y2 = 13 at (3,-2).
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
First, look for the line containing points (0,0) and (3,-2). Assuming point (3,-2 )is also on the circle, find the line perpendicular to the just found line and containing the point (3,-2).

Something worth checking: Is (3,-2) on the circle x%5E2%2By%5E2=13?
3%2A3%2B%28-2%29%5E2=13
9%2B4=13, YES.

Line (0,0) to (3,-2) is y=-%282%2F3%29x;
A line perpendicular is y=%283%2F2%29x%2Bb. THIS line must contain(3,-2).
b=y-%283%2F2%29x
b=-2-%283%2F2%29%2A3
b=-2-9%2F2
b=-4%2F2-9%2F2
b=-13%2F2
Line tangent to circle at (3,-2) is highlight%28y=%283%2F2%29x-13%2F2%29.

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C-sqrt%2813-x%5E2%29%2C%283%2F2%29x-13%2F2%29