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Unformatted text preview: The slope of the tangent line to the parabola at P is 2 x . This tangent line is tangent to the circle at that point, too, so is perpendicular to the radius joining the center of the circle and P . The slope of that radius is therefore -1/2 x . Call the angle between that radius and the horizontal q, so q = arctan(1/2 x ). (The change in sign comes from the orientation of q .) Now we can see that x 2 = y = 1 + sin q = 1 + sin(arctan(1/2 x )) = 1 + 1/ Ö(1+4 x 2 ). After straightforward algebra, the only significant solution is x 2 = (7 + Ö 17)/8, or x = 1.17914. .. With the center of the circle at ( a , b ) we have b = 1 and a = x + cos q = x + 2 x / Ö(1 + 4 x 2 ) = 2.0997. .. this page....
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- Spring '10
- Combinatorics, Nathan Pauli, Daniel J. Statman, different solution techniques