You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.

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We already know one point on the tangent line, so to find its equation we require its slope. We can find the slope either by getting another point on the line or by some other means. We shall find the slope of a line which runs perpendicular to the tangent line and then use the fact that the product of the slopes of two ...

Solution Summary

This shows how to find the equation of a tangent line to a circle.

... Therefore, the tangent line equation is y − f (8) = m( x − 8). Now find f (8) = (2 *8 + 4)2 − (2 * 8 − 4) 2 = 256. So the equation of the tangent line is. ...

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