To solve this equation, we can start by simplifying both sides:

25 - y^2 = 8(x^2 - 4024x + 4048144)

Next, we can distribute the 8 on the right side:

25 - y^2 = 8x^2 - 32192x + 32385152

Now, let's move all the terms to one side to get a quadratic equation:

8x^2 - 32192x + 32385152 - 25 + y^2 = 0

8x^2 - 32192x + 32385127 + y^2 = 0

Now, we can rearrange the equation to get it in the form of a quadratic equation:

8x^2 - 32192x + (32385127 + y^2) = 0

This equation represents a parabola.