Ellipse justification

Hey guys, this is my first time hear. I'm havin abit of trouble with this problem for school, i just can't seem to understand it. Can someone please walk me through both what the question means and how to answer it?

Thanks

Attached is the problem:

Rope is a + b which remains constant

When rope is such that the stick is at P₂ then the Rope goes from F₁ to P₂ and back to F₂

The length of the rope is therefore F + F + A - F + A - F = 2A

So a + b = 2A

But a = b so 2a = 2A

a = A

Consider right angled triangle with sides F, B and a = A

Then by Pythagoras

A² = B² + F²

F² = A² - B²

F = sqrt(A² - B²) as required