The curve C has equation 2x² + 2xy + 5y² = 20.

The points on C for which both the x and y coordinates are integers are the vertices of a convex polygon P.

Find the exact perimeter of polygon P.

To find solutions consider this as a quadratic in x: (2)x^2+(2y)x+(5y^2-20)=0.  The discriminant of this is 160-36y^2 which is only a perfect square for y= +/- 2.

Edited on February 19, 2024, 1:58 pm

Posted by Jer on 2024-02-19 07:59:22