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November 27th, 2007, 04:53 PM   #1
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Tangent Line and Point of Tangency

If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b, show that:

(a) r^2(1 + m^2) = b^2

(b) The point of tangency is the point (-(r^2m/b), (r^2/b))

(c) The tangent line is perpendicular to the line having the center of the circle and the point of tangency.
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November 27th, 2007, 06:46 PM   #2
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Hint: use the equation of the tangent to substitute for y in the equation of the circle. The resulting quadratic in x must have a zero discriminant (so that it has a unique solution).
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