GivenP(-2, 3) and circle (x-3)^2 + (y-3)^2 = 9, find the tangents (of the circle) throughP.

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- Jul 15th 2010, 10:26 AMMATNTRNGAnalytical Geometry
Given

*P*(-2, 3) and circle (*x*-3)^2 + (*y*-3)^2 = 9, find the tangents (of the circle) through*P*. - Jul 15th 2010, 12:08 PMred_dog
A line passing thruogh the point P and havinf the slope m has the equation

The line must intersect the circle in a single point, so the system of equations formed by the equation of the line and the equation of the circle must have only one solution.

Replace y in the equation of the circle and you'll find a quadratic equation:

This equation must have equal roots. For this, the discriminant must be 0.

.

Replace m in the equation of the line with these two numbers and you'll find two tangents line to the circle.