Pair of tangents drawn from a point to given circle

Let the point be (x1,y1) and the circle be x² + y² = a²

Two tangents can be drawn.

The tangent will be of the form y = mx+a√(1+m²)
And the two values of m for the pair is to be found by solving the quadratic equation
m²(x1²-a²) -2mx1y1 +(y1²-a²) = 0