Question

What is the equation of the following graph?

Answer 1

This is a vertical ellipse since it's taller than it is wider. That means that y is the transversal axis, aka the major axis. The formula for this type of ellipse is
`((x-h)^2)/(b^2)+((y-k)^2)/(a^2)=1`

where h and k are the center of the ellipse and a is the number of units from the center along the minor axis to the outside of the ellipse and b is the number of units from the center along the major axis to the outside of the ellipse. Here, our h and k are, respectively, (0, -3), a = 1 and b = sqrt(3). Fitting those values into our formula we have the equation as

`(x^2)/(√(3))+((y+3)^2)/(1) =1`.

That's your answer!