SOLUTION: write the equation of this circle the equation of the line tangent x^2+y^2=225 at (9,-12) please help

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Question 870460: write the equation of this circle
the equation of the line tangent
x^2+y^2=225 at (9,-12)
please help
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
What you MEAN is, find the equation of the tangent line to the circle at the point (9,-12).

The circle is x%5E2%2By%5E2=225.
The center is (0,0) and the radius is sqrt(225) but not necessary to solve the problem. The center point IS necessary.

Is the given point really on the circle?
9*9+144=225?
81+144=225, Yes.

The slope of the line containing (0,0) and (9,-12) is -4%2F3; so the line perpendicular must have slope 3%2F4. Note that (0,0) and (9,-12) forms a radius of the circle.

We want the line so that y=%283%2F4%29x%2Bb and contains (9,-12). We can find the value for b.
b=y-mx
b=-12-%283%2F4%299
b=-12-27%2F4
b=-48%2F4-27%2F4
b=-75%2F4
Equation: highlight%28y=%283%2F4%29x-75%2F4%29.