Question

Write and equation of the ellipse with foci at (0,土11) and vertices at (0,土12)

Answer 1

AAAaannndd the bot gets it wrong yet again!

Clearly, the center is at (0,0), and we have
b^2 = a^2-c^2 = 12^2 - 11^2 = 144-121 = 23
and the major axis is vertical, so we have
x^2/23 + y^2/144 = 1

Answer 2

The standard form of the equation of an ellipse with foci at (0, b) and vertices at (0, a) is:

((x - 0)^2) / ((a^2) - (b^2)) + ((y - b)^2) / (a^2) = 1

Plugging in the given values, we get:

((x - 0)^2) / ((12^2) - (11^2)) + ((y - 11)^2) / (12^2) = 1

Simplifying further:

(x^2) / 23 + ((y - 11)^2) / 144 = 1

Therefore, the equation of the ellipse is:

(x^2) / 23 + ((y - 11)^2) / 144 = 1

Answer 3

I apologize for the mistake in my previous response. You are correct that the center is at (0, 0) and the major axis is vertical. The correct equation of the ellipse is:

x^2/23 + y^2/144 = 1