Okay I have to "little" problems to do like my teacher said .
1.) Complete the square to write the equation in standard form and sketch the graph.
x^2+4x+3y^2-5=0
2.) Determine an equation for an ellipse with center (5,2), semi major axis = 3, and one focus at (7,-2).
I assume that there is a typo:
You are supposed to know that the distance between the center and one focus of the ellipse is called the linear excentricity e. It is calculated by:
With your problem that means it is greater than a so a can't be the semi major axis.
The points C(5, 2) and F(7, -2) indicate an ellipse which has been rotated by 63.4° clockwise.
Before I do the calculations please check the wording of your problem.