# Equation of a Line Tangent to a Circle

(a) Consider the circle that has its center at the point (2, -3) and passes through the point (5, -1). Find the radius of this circle, and find the point-slope and slope-intercept forms of the equation of the line which is tangent to this circle at the point (5, -1). In your solution, use only algebra and the fact that a line which is tangent to a circle is perpendicular to the line that passes through the center of the circle and the point of tangency.

(b) Do the same for a circle that has its center at the point (h, k) and passes through the point (x_0, y_0), where h, k, x_0, y_0 are real numbers such that the conditions h = x_0 and k = y_0 are not both satisfied.

(c) In part (b) above, why do we specify that the conditions h = x_0 and k = y_0 are not both satisfied?

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#### Solution Summary

A complete, detailed solution for part (a) and part (b) is provided in the attached .pdf file, where all the steps in the mathematics are shown and explained. Also, the reason for the condition specified in part (b) is explained in the .pdf file.