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Why is c less than b? In mathematical problems, two straight lines at the intersection of normal elliptic equations are hammered against each other. How did you get it?
This is an existential problem, as long as the largest angle in the ellipse exceeds the right angle.

When p is at the top and bottom vertices, ∠F 1PF2 is the largest, and p is inside the ellipse, so ∠F 1PF2 is strictly greater than the right angle.

Then ∠ f 1po > 45, so c = op < of1= B.