Question

Write the equation in standard form for the ellipse with vertices (-10, -19) and (10, -19),

and co-vertices (0, -12) and (0, -26).

Answer 1

To write the equation of the ellipse in standard form, we first find its center, semi-major axis, and semi-minor axis:

Center: The midpoint between the vertices is (0, -19).

Semi-major axis: The distance from the center to a vertex is 10.

Semi-minor axis: The distance from the center to a co-vertex is 7.

Using these values, the standard form equation of the ellipse is:

(x^2/100) + ((y + 19)^2/49) = 1

This equation is simplified and easier to read.