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Mathematics-Online problems: | ||
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.
Answer:
, | |
, | |
(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: