Circle, tangent line, and a point not on the circle
Suppose you have a unit circle and a point P with coordinates (4, 2). The task is to find the tangent points.
Here are my steps:
1. Name the coordinates of the tangent point in quadrant II as (r, s).
2. The slope of the tangent line is m = (s/r)
3. Rewrite the tangent point as (r, sqrt(1-r^2))
This is as far as I get before everything breaks down. Am I right so far?
4. My next step is to try to solve for r by using y = mx + b and the two points. But I end up with an ugly equation involving rational terms, radial terms, etc. and always end up with the wrong answer even when I cheat with a graphing calculator. Any idea what I'm doing wrong?