Picking points on circles

You can find an infinite number of nice fractions that work for the coordinates of the points on a unit circle (a circle with a radius of 1). 

Using the formula to find a few points, let m = 2, for example. Then 

The formula for these points on the unit circle comes from solving a system of equations. 

The Problem Find the coordinates of the points on the unit circle with its center at the origin that are shared with any line going through the point (-1,0) on that circle. Distinguish between the different lines that go through (-1,0) by letting m represent the slopes of the different lines. 

Find the common solution of the circle, x2 + y2 = 1 and the line y = mx + b. The particular line that goes through the point (-1,0), has an equation that can be written a little more specially. Finding the slope of this line, m, using the slope 

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