Locus of Intersection of Diagonals of a Trapezium

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One of two parallel sides of a trapezium is given in magnitude and position, the other in magnitude. The sum of the remaining two sides is given.

The problem with this example is that Geometry Expressions does not allow you to enter the lengths of both parallel sides in addition to the lengths of each of the remaining sides, so some preparatory work is needed. We first constrain the problem, missing out the length of one of the non-parallel sides, but adding an angle. We then derive the length of the fourth side in terms of the angle, and solve.

We see that the resulting figure is an ellipse.

Note: A trapezium is the British name for a trapezoid.

Expressions

Name Input
Locus Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image