Find an equation in standard form for the ellipse with center at (6, 9), horizontal major axis of length 6 and passes through the point (8, 8).

Answer 1

(x-6)^2/a^2 + (y-9)^2/b^2 = 1 plug in 6/2=3 then x=8 and y=8 to get the minor axis/2 = b

(8-6)^2/3^2 + (8-9)^2/b^2 = 1

4/9 + 1/b^2 = 1

1/b^2 = 1-4/9 = 5/9

b^2 = 9/5

b = 3/sqr5

(x-6)^2/9 +5(y-9)^2/9 = 1

or

(x-6)^2 +5(y-9)^2 = 9