Answer:
(x, y) = (-ln/(l²+m²), -mn/(l²+m²))
Step-by-step explanation:
The given equation for the tangent line can be written in standard form as ...
lx +my = -n
The perpendicular line through the origin (the center of the circle) is ...
mx -ly = 0
The point of intersection of these lines is the point of tangency. It can be found a number of ways. Cramer's rule offers perhaps the simplest:
(x, y) = (l, m)×(-n/(l²+m²))
(x, y) = (-ln/(l²+m²), -mn/(l²+m²))
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In order for this point of tangency to be on the circle, we must have ...
a² = n²/(l²+m²)
which means another way to write the coordinates of the tangent point is ...
(x, y) = (-a²l/n, -a²m/n)
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Attached is an example of the problem and the solution.
