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 an equation for an ellipse centered at the origin with vertex (-6, 0) and co-vertex (0, 4) is:

[(x + 6)^2 / a^2] + (y^2 / b^2) = 1

where 'a' is the distance from the center to the vertex (in this case, 6) and 'b' is the distance from the center to the co-vertex (in this case, 4).

Substitute the values of a and b into the equation:

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

Simplify:

[(x + 6)^2 / 36] + (y^2 / 16) = 1

Therefore, the equation in standard form is:

[(x + 6)^2 / 36] + (y^2 / 16) = 1