The equation of a curve is $y=16-ax-x^{2}$, where $a$ is positive constant.

1. Expand the given completed square form

$25 - (b+x)^2 = 25 - (b^2 + 2bx + x^2)$
$= (25 - b^2) - 2bx - x^2$

2. Compare the constant term to find $b$

Comparing the constant term with $16 - ax - x^2$:
$25 - b^2 = 16$
$b^2 = 9$
Since $b$ is a positive constant, $b = 3$.

3. Compare the coefficient of $x$ to find $a$

Comparing the coefficient of $x$:
$-2b = -a$
$a = 2(3) = 6$

1. Find the value of $b$ from part (a) to complete the expression for $y$

Expanding $25 - (b+x)^2$ gives $25 - b^2 - 2bx - x^2$.
Comparing the constant term with $y = 16 - ax - x^2$:
$25 - b^2 = 16$
$b^2 = 9$
Since $b$ is positive, $b = 3$.
Thus, $y = 25 - (x+3)^2$.

2. State the maximum value of $y$ and the corresponding value of $x$

From $y = 25 - (x+3)^2$, the maximum value occurs when the squared term is zero, i.e., $(x+3)^2 = 0$.
Maximum value of $y = 25$.
This occurs when $x + 3 = 0 \implies x = -3$.

1. Set up the inequality for $y > 0$ using the expression from part (a)

From part (a), $y = 25 - (x+3)^2$.
For $y$ to be positive, $25 - (x+3)^2 > 0$.

2. Solve the quadratic inequality

$(x+3)^2 < 25$
$-5 < x+3 < 5$

3. Find the final range of values for $x$

$-5 - 3 < x < 5 - 3$
$-8 < x < 2$