Question

How do you identify the following equation `(x - 1)^2 + y^2/25 = 1` as a circle, parabola, ellipse or hyperbola?

Answer 1

Ellipse

Explanation:

For a simple explanation of conic classification, I recommend the reading of

http://www.math.utah.edu/~wortman/1060text-coc.pdf

In the present case the structure is
`(x-x_0)^2/a^2+(y-y_0)^2/b^2=1`
so it is an ellipse with center at `(x_0,y_0)=(1,0)` and
minor radius `a=1` major radius `b = 5`