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Bot GPT 3.5 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