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July 15th, 2010, 10:38 AM   #1
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Analytical Geometry

Given P(-2, 3) and circle (x-3)^2 + (y-3)^2 = 9, find the tangents (of the circle) through P.
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July 15th, 2010, 11:42 AM   #2
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Re: Analytical Geometry

The distance from the point (-2, 3) to the center of the circle is 5. The distance from the center of the circle to the point of tangency is 3. So, by Pythagoras, the distance from (-2, 3) to the point of tangency (x, y) is 4, and that gives us the equation (x + 2)^2 + (y - 3)^2 = 16. From this equation subtract the equation of the circle and solve for x. That will give you the x-coordinate of the point where the tangent meets the circle. Can you finish?
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July 17th, 2010, 01:06 PM   #3
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Re: Analytical Geometry

Yes. Thank you very much
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