My Math Forum Tangent Line and Point of Tangency

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 November 27th, 2007, 04:53 PM #1 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 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.
 November 27th, 2007, 06:46 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,633 Thanks: 2080 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).

 Tags line, point, tangency, tangent

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# slope of line of tangency from point (-4,0) to circle x^2 y^2 = 1

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