This is a horizontal equation of an ellipse in general conic form and a graph. As you can see, both x and y terms are squared and positive, but now have different coefficients.
To form a vertical ellipse, the a and b are switched around in the equation so that now the x term is above the smaller number and the y term is above the larger one. The vertices would then change accordingly to be (h, k - a) and (h, k + a), for example.
