Answer
It is an ellipse.
See Graph I for the graphing of the equation.
Work Step by Step
For $\frac{(x-1)^2}{49} + \frac{(y+2)^2}{25} = 1$, it is in the form of an ellipse.
The center is at (1. -2) with a = 7 and b = 5.
The highest point is at (1, 3) and the lowest point at (1, -7).
The leftmost point is at (-6, -2) and the rightmost point at (8, -2).
See Graph I for the graphing of the equation.