Precalc
posted by Grace .
An ellipse has this Cartesian equation:
((x2)/5)^2 + ((y4)/3)^2 = 1
Find the focal radius
Find the eccentricity
Write the parametric equations for the ellipse
Transform into the form, Ax^2 + By^2 + Cx + Dy + E = 0

I don't know which author you use, but focal radius can be defined in more than one way
http://www.mathwords.com/f/focal_radius.htm
for yours,
a = 5, b = 3
your ellipse will be horizontal, and
b^2 + c^2 = a^2
9+c^2 = 25
c^2 = 16
c = 4
eccentricity = c/a = 4/5 = .8
parametric equations:
x2 = 5coss t > x = 5cost + 2
y4 = 3sin t > y = 3sint + 4
original:
(x2)^2 /25 + (y4)^2 / 9 = 1
multiply by 225
9(x2)^2 + 25(y4)^2 = 225
9(x^2  4x + 4) + 25(y^2  8y + 16) = 225
I am sure you can finish it.