Question: 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.

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. See the figure.

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If the equation of the circle is and the equation of the tangent line is, show that:

If the equation of the circle is x2 + y2 = r2 and the equation of the tangent line is y = mx + b, show that:

(a) r2 (1 + m2) = b2

The quadratic equation x2 + (mx + b) 2 = r2 has exactly one solution.

(b) The point of tangency is (-r2m/b, r2/b).

(c) The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.

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