what is an equation in standard form of an ellipse centered at the origin with vertex (-6, 0) and co-vertex (0,4)?

Answer 1

The standard form of the equation of an ellipse centered at the origin with vertices (±a, 0) and co-vertices (0, ±b) is:

(x^2/a^2) + (y^2/b^2) = 1

In this case, the vertices are (-6, 0) and (6, 0) and the co-vertices are (0, 4) and (0, -4).

Since the vertices are on the x-axis, a = 6 and since the co-vertices are on the y-axis, b = 4.

Plugging these values into the standard form equation, we get:

(x^2/6^2) + (y^2/4^2) = 1

Simplifying further:

x^2/36 + y^2/16 = 1

Therefore, the equation of the ellipse in standard form is:

x^2/36 + y^2/16 = 1