Qhich of tge following nonlinear inequalities is graphed below

The answer is A.
It is an equation of an ellipse, where y is the major axis. You know the major axis by the greatest number, if the greatest number is under the y, so this means the axis of the ellipse is parallel to the y axis. And here as the ellipse passes through the origin, the y axis is the major axis of the ellipse.
And to know which inequality you choose, A, C or D as they look similar, you look at the shaded part. The shaded part contains only the inner part and not the borders. So it should be the region that is less than the given value 1.

Hope this helps.