Let S ≡ x2 + y2 − a2 = 0 be a circle and P(x1, y1) be an external point to the circle, so that
S11 = x12 + y12 - a2 > 0
we know that y = mx + a √1 + m2 touches the circle S ≡ x2 + y2 − a2 = 0. This line passes through P(x1 , y1)
Equation (1) is a quadratic equation in m whose discriminant is
Therefore, the quadratic equation [Eq. (1)] in m has two distinct roots, say m1 and m2, so that there are two tangents through (x1, y1) with slopes m1 and m2 and
