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

May 24, 2016

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
${\left(x - {x}_{0}\right)}^{2} / {a}^{2} + {\left(y - {y}_{0}\right)}^{2} / {b}^{2} = 1$
so it is an ellipse with center at $\left({x}_{0} , {y}_{0}\right) = \left(1 , 0\right)$ and
minor radius $a = 1$ major radius $b = 5$