I am finding it difficult the following problem:
I have the ellipse (3x^2 + 5y^2 = 75) and I have solved it as follows:
Foci: + and - (sqrt(10), 0)
Directrices: + and - 5*sqrt(10)/2
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!