Write the ellipse equation if:

Question

The points A(0,2) and B(-6,2) belong to the ellipse. 

Answer 1

If the points (0,2) and (-6, 2) belong to the ellipse you can conclude that the center of the ellipse is at  (-3,2)

 

This will give you the equation:

 

((x+3)^2)/a^2 + ((y-2)^2)/b^2 = 1

 

We are not given any information on which axis is your major axis. The above equation assumes that the major axis is horizontal, therefore a^2=9 and b^2 is a positive number smaller than 9.  

 

If you assume that the major axis is vertical then the equation will be

 

((x+3)^2)/b^2 + ((y-2)^2)/a^2 = 1

 

Where b^2=9 and a^2 is anything greater than 9.