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54. 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.
If the equation of the circle is and the equation of the tangent line is , show that:
a.
[Hint: The
b. The point of tangency is .
c. The tangent line is perpendicular to the line containing the center of the circle and the point of tangency
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