I am finding it difficult the following problem:

I have the ellipse (3x^2 + 5y^2 = 75) and I have solved it as follows:

a=5

b=sqrt(15)

Foci: + and - (sqrt(10), 0)

Directrices: + and - 5*sqrt(10)/2

Eccentricity: sqrt(10)/5

Center: (0,0)

Vertices: (5,0) (-5,0) (0, sqrt(15)), (0, -sqrt(15))

Now I must equate PF=ePd to the above information. I must show all the workings to "show that the equation holds where the conic intersects with the x-axis". The difficulty is placing all this square roots to fit the algebra. They prefer it that we put all of this in square roots, not decimals. Pity!

Then I must describe the following translation in terms of the above ellipse: 3x^2 + 12x + 5y^2 - 10y -58 = 0 . I must solve the algebra to find exact coordinates of the points for center, vertices, axes of symmetry and and slopes of any asymptotes.

I tried to solve this for the center and found the answer (-6,5) but it does not look right so I can not continue.

Finally, must I write parametric equations for the two ellipses.

Many thanks for some help is someone can!

Brigitte