Alan

Here's my attempt at an analytical answer:

I should have written: This is the value of k at the minimum area.  The minimum area itself is $k\pi$

I've just noticed something went wrong with the display of equation (3)! It should be $xp = \frac{a^2}{a^2-b^2}$

Like so:

Can you take it from here?

If you mean in the calculator on the home page here, then yes, e.g. typing 7! will result in 5040.

See reply at https://web2.0calc.com/questions/please-help_81386

This should help:

Can you take it from here?

"Let x and y be real numbers such that 2(x^2 + y^2) = x + y + 1. Find the maximum value of x - y"

Use Pythagoras' theorem. 

One leg of the right-angled triangle is r(the radius); the other leg is 4.5; the hypotenuse is (r+1.5).

The following should help you answer that:

This can be written as $\frac{x^2}{13^2}+\frac{y^2}{5^2}=1$, so the semi-major axis is 13, the semi-minor axis is 5, and its centred on (0, 0).

Can you take it from here?

As follows: