What is the equation of the line tangent to f(x) = 5 - x ^ 2 * a at x = - 2 ?

According to the Pythagorean Theorem, x^2 + y^2 = hyp^2.

Let x = 5cm be one leg.

If the hyp is twice as long as the other leg, then hyp = 2y.  

Then x^2 + y^2 = hyp^2 becomes

       (5 cm)^2 + y^2 = (2y)^2.  We need to solve this for y.
                          
                                                                                         25 cm^2
25 cm^2 + y^2 = 4y^2, or 25 cm^2 = 3y^2.  Then y^2 =
                                                                                               3

and y = + sqrt( [25 cm^2] / 3 ), or   y = + 5 / sqrt(3), or y = 5sqrt(3) / 3.

The "other side" thus has length   y = 5sqrt(3) / 3  

and the hyp has length 2y = 2 [ 5sqrt(3) / 3 ]  =  10 sqrt(3) / 3