Precalc ellipse in standard form

Question

Major axis vertical with length 8; length of minor axis=4; center: (-8,4)

Answer 1

IF this had been an ellipse centered at the origin the equation would be

x^2/16 + y^2/64 = 1

to shift the center change it to

(x+8)^2/16 + (y-4)^2/64 = 1

or if you want to eliminate fractions multiply by 64 to get

4(x+8)^2 + (y-4)^2 = 64

or if you want to eliminate parentheses

4x^2 + 64x + 256 + y^2 - 8y + 4 = 64

combine the constant terms

4x^2 + 64x + y^2 -8y = -190

but leaving the equation as

(x+8)^2/4^2 + (y-4)^2/8^2 = 1 is probably best, as you can read the center and semi-axes off it directly

Answer 2