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Inside a Parabola

Age 14 to 16 Short Challenge Level:

The points where the parabola $y=k^2-x^2$ crosses the coordinate axes are joined to form a triangle.

The area of the triangle is 64 square units. What is the value of $k$?

This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.