The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the POINT OF TANGENCY.
If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show that:
(a) r^2(1 + m^2) = b^2
HINT GIVEN FOR PART A:
The quadratic equation x^2 + (mx + b)^2 = r^2 has exactly ONE SOLUTION.
(b) The point of tangency is the point (-r^2m/b, r^2/b).
(c) The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.
(d) Draw a tangent line to a circle in the xy-plane.
Use r to represent the radius.