okay I attached the graph! so the question is:
determine the equation of the following ellipse in standard form and in general form.
okay what formula would I use like I am not even sure how to begin this question ?
Just a guess, I don't think the jpg is an ellipse.
The general form for an ellipse (with major or minor axes along the x and/or y directions) is
$\displaystyle \frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1$
where the center of the ellipse (where the major and minor axes cross) is the point (h, k), and a and b are the semi-axis major or minor depending on the orientation of the ellipse.
In your case the center is: (2, 3), the semi-axis major is along the x direction so a = (3 - -3)/2 = 6/2 = 3, and the semi-axis minor is along the y direction so b = (5 - 1)/2 = 4/2 = 2. Thus your ellipse is:
$\displaystyle \frac{(x - 2)^2}{3^2} + \frac{(y - 3)^2}{2^2} = 1$
$\displaystyle \frac{(x - 2)^2}{9} + \frac{(y - 3)^2}{4} = 1$
-Dan