Note that the right side has to be a 1 to be in standard form.  The point ( h, k ) is called the center of the ellipse.

To graph the ellipse all that we required are the left most, right most,  top most and bottom most points.  Once we have those we can sketch in the ellipse.  Here are formulas for determining these points.

right most point : ( h + a, k )

left most point : ( h - a, k )

top most point : ( h, k + b )

bottom most point : (h, k - b )

Note that a refer to the square root of the number under the x term and it is the amount which we move right & left from the center.  Also, b refer to the square root of the number under the y term & it is the amount which we move up or down from the center.