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!
So, please tell me if this is correct:
(x+2)^2/(75/3) + (y-1)^2/75/5 = 1 ... etc
Does this make that the transformation is to the new ellipse center (-2, 1)? So that will be 2 units to the left and 1 unit to the top?
Thank you so much on this part. Maybe I can progress.
Ok, please tell me if these following are correct:
vertices: (3,0), (-7,1), (0, 1+sqrt(15)), (0, 1+(-sqrt(15))
axes of symmetry: (does this means the minor and major axis of symmetry? if yes, how do I mention the exact coordinates as the axis exend from the points of the vertices mentioned above.)
slopes of any asymptotes: is there none in this example, since they are only on the hyperbolas?
Thank you again!
For instance: then the major axis is determined by