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Solution to the problem of the (previous) week
Problem:The figure shows a quadrilateral bounded by two tangent lines to a parabola and their two normal lines. The parabola is described by the equation
Determine the points and as well as the area of the shaded region.
(The results should be correct to four decimal places.)
Solution:The straight line joining the center point and the point has slope . This line is perpendicular to the tangent line which has slope . Thus, we have
The area is half the product of the lengths of the diagonals: