Question

Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2)

Answer 1

it is helpful to make a drawing

Answer 2

Formula for an ellipse:

\[\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]\(a = \) length of semi-major axis
\(b = \) length of semi-minor axis
\((h,k)\) center of ellipse

The way I remember this is to think of the ellipse as a stretched circle. At one of the vertices, say (10,0), only one of the variables will be contributing to the sum, so the divisor is just the x value squared. At one of the co-vertices, only the y component contributes to the sum, so the divisor is the y value squared. Once you remember the general form, you can add in h and k to translate it to a different spot on the coordinate plane away from the origin.