Standard Form: x^2/a^2+y^2/b^2=1. To put in standard form, either divide or complete the square.

Steps to sketching an Ellipse:

Find the major axis which is the variable with the largest denomenator.

Find the minor axis which is the variable with the smallest denominator.

Find the vertex which is the square root of the largest denominator and to put in point form if the major axis is x the answer goes in the x spot and vise versa.

Find the other intercept which is the square root of the smallest denominator, put in point form.

Find the length of the major axis which is two times the square root of the largest denominator.

Find the length of the minor axis which is two times the square root of the smallest denominator.

The focus is always on the major axis and is a point.To find the focus, vertex, or other intercepts, use the formula: smallest denominator=largest denominator-focus^2 or other intercept^2=vertex^2-focus^2.

Example:

(x^2/4)+(y^2/9)=1

The y axis is the major axis because it has the largest denominator. The x axis is the minor axis because it has the smallest denominator. The square root of 9=+/-3, which gives you the vertices of (0,3) and (0,-3). The square root of 4=+/-2, which gives you the other intercepts of (2,0) and (-2,0). Two times the square root of 9(largest denom.)=2(3)=6. Two times the square root of 4(smallest denom.)=2(2)=4. Focus: 4=9-focus^2
-5=-f^2
Focus= +/- square root of 5
(0, square root of 5) and (0, -square root of 5)