Need help with Maximum/Minimum Problems...

I'm having some issues with solving these 2 problems. (Crying)

The first one is as follows:

**Find the value of a for which the area of the triangle formed by the tangent (y=a^2 - 2ax + 4) and the co-ordinate axes will be minimum.**

I calculated the distances of the side and base of the triangle by finding the intercepts of the tangent.

Heres what I got: side = (a^2 + 4)/2 and base = a^2 + 4

Therefore, my main equation for the area was 1/2*side*base

I simplified the area equation, differentiated it (using quotient rule) and got a= +2 or -2

I tested both with the first derivative, and found a=2 produced the local max.

Therefore, the area would be 8 units squared

However the answers say the area is 2/3*\sqrt{3}

The second question is similar:

**Find the maximum area of a right triangle with a hypotenuse of 16cm**

my starting equation was y^2 = \sqrt{256-x^2}

subbed into the area equation and differentiated, i reached a dead end...i think i ended up with the first derivative test screwing up...

the answer is apparently 64cm^2

Any help on these 2 questions? Ive been working on them for ages and keep repeating the same steps to no avail...

Thanks!(Nod)