Tangent Lines without Calculus
(University of New Mexico)

A tangent line to a circle is a line that passes through just one point of the circle and is perpendicular to the radius line. Find the equation of the tangent line to the circle defined by at the point (-1, 5).

The student should be able to sketch the figure to picture the problem. The slope of the segment joining the center of the circle (2, 1) to the point (-1, 5) is -4/3, and so the slope of a perpendicular line is 3/4. The equation for the line through (-1, 5) with this slope is .