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See the problem Isosceles.

The triangle OPA has a vertex O at the origin and OA along the x axis, such that P has coordinates (x, y) and A has coordinates (2x, 0). By moving the position of the point P infinitely many isosceles triangles can be formed all having an area of 12 square units. What is the locus of P such that the area of the triangle OPA is 12 square units? In the Java applet below, the point P is controlled by sliding the red point along the red line. If the red point disappears from view, simply press reload.