SOLUTION: Find the equations of the lines through (7,-4) passing at a distance 1 from the point (2,1).

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Question 732148: Find the equations of the lines through (7,-4) passing at a distance 1 from the point (2,1).
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A circle with center at (2, 1) and radius 1 intersects with the line(s) which contains (7, -4). The circle is %28x-2%29%5E2%2B%28y-1%29%5E2=1.

There will be two right triangles. Consider one of them. The length from (7, -4) to the circle center (2, 1); The length from circle center to the line's point of tangency on the circle, which is size 1; the unknown length from the point of tangency to the point (7, -4). We can use pythagorean theorem to find the size of this unknown length. Could we then use distance formula to find this point of tangency on the circle? Transforming the equation of the circle to one of its functions of y in terms of x may help in selecting a general point on the cirlce, some (x, f(x)). I did not try solving this, but am only trying to think of the method.