Find an equation of the ellipse that has center (0,-5),a minor axis of length 12, and a vertex at (0,9).

Answer 1

(x-h)^2/a^2 + (y-k)^2/b^2 = 1 where (h,k) = center = (0,-5) a=12/2= 6, vertex = (0,9) i.e. major axis =28, semi axis= (9--5)= 14=b

x^2/36 + (y+5)^2/196 = 1

probably stop here where you can read off the center and semi axes, or go further and 'simplify" eliminating fractions

196x^2 + 36(y+5)^2 = 36(196)

196x^2 + 36(y^2 +10y +25) = 7056

196x^2 + 36y^2 +360y + 900 = 7056

196x^2 +36y^2 +360y = 7056-900

196x^2 +36y^2 + 360y = 6156