1. The problem states that the relationship between $y$ and $x$ is given by the formula $$y = \frac{k}{x^2}$$ where $k$ is a constant. 2. We are given that when $y = 8$, the equation becomes $$8 = \frac{k}{x^2}$$. 3. To find $k$, multiply both sides by $x^2$: $$8 \times x^2 = \cancel{x^2} \times \frac{k}{\cancel{x^2}} \implies 8x^2 = k$$ 4. So, the constant $k$ is $$k = 8x^2$$. 5. Now, to find the value of $y$ when $x = h$, substitute $k$ back into the original formula: $$y = \frac{k}{h^2} = \frac{8x^2}{h^2}$$. 6. If $x = h$, then: $$y = \frac{8h^2}{h^2}$$ 7. Simplify by canceling $h^2$: $$y = \frac{8\cancel{h^2}}{\cancel{h^2}} = 8$$ **Final answer:** When $x = h$, the value of $y$ is $$y = 8$$.