Originally Posted by

**Unknown008** 1. Yes, the domain is negative infinity to infinity.

The range, however is y > 0. The graph never touches the x-axis.

2. Be careful!

Let y be the longer length, and x be the shorter length.

Then;

$\displaystyle a^2 = h^2 + x^2\\

a^2 = k^2 + y^2$

x + y is what you're looking for.

So,

$\displaystyle x = \sqrt{a^2 - h^2}$

$\displaystyle y = \sqrt{a^2 - k^2}$

$\displaystyle x + y = \sqrt{a^2 - h^2} + \sqrt{a^2 - k^2}$

That's not too easy on the eyes though. Let's take trigonometry.

$\displaystyle cos(75) = \frac{y}{a}$

$\displaystyle cos(45) = \frac{x}{a}$

So;

$\displaystyle y = acos(75)$

$\displaystyle x = acos(45)$

$\displaystyle x + y = a(cos(75) + cos(45))$