1. **Problem:** Find the equation of the parabola with vertex at (5, -2) and focus at (-5, -2). 2. **Recall the formula:** For a parabola with a horizontal axis, the vertex form is $$ (y-k)^2 = 4p(x-h) $$ where $(h,k)$ is the vertex and $p$ is the distance from the vertex to the focus. 3. **Identify values:** Vertex $(h,k) = (5, -2)$. Focus $(-5, -2)$ lies on the same horizontal line, so the parabola opens left or right. 4. **Calculate $p$:** Distance from vertex to focus along x-axis is $$ p = -5 - 5 = -10 $$ (negative because focus is to the left). 5. **Write the equation:** Substitute into the formula: $$ (y - (-2))^2 = 4(-10)(x - 5) $$ which simplifies to $$ (y + 2)^2 = -40(x - 5) $$ 6. **Interpretation:** This is the equation of the parabola with vertex at (5, -2) opening to the left. **Final answer:** $$ (y + 2)^2 = -40(x - 5) $$