Refer to Problem 65. The line x 2y + 4 = 0 is tangent to a
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Refer to Problem 65. The line x − 2y + 4 = 0 is tangent to a circle at (0, 2). The line y = 2x − 7 is tangent to the same circle at (3, −1). Find the center of the circle.
Data from problem 65
If the equation of a circle is x2 + y2 = r2 and the equation of a 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
(c) The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.
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Related Book For
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry
ISBN: 9780137945139
5th Edition
Authors: Michael Sullivan
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