The two orthogonal parabolas:
y=2x^2+a
x= 2y^2+b
intersect at four distinct points.
These four points are on the same circle of area 10.
Given that a, b < 0, determine the minimum value of ab.
Yesterday, I tried several algebraic manipulations without success.
I tried using Desmos to find a solution graphically. It appears that there is probably only one solution.
So rather than the minimum value for ab, there is probably only one value.
From manually adjusting parameters it looks like ab is approximately 9.3.
https://www.desmos.com/calculator/jcvuypg3ya
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Posted by Larry
on 2025-03-14 08:10:11 |
Graphical approximation
