Write the equationn of the ellipse 16x2 9y2 128x 18y 121

Write the equationn of the ellipse 16x^2 + 9y^2 -128x - 18y +121 = 0 in standard form (x-h)^2/a^2 + (y-k)^2/b^2 = 1 Where

Solution

16x^2 +9y^2 -128x -18y +121 =0

grouping together x and y terms :

16(x^2 -8x) + 9(y^2 -2y) +121 =0

16(x-4)^1 - 256 +9(y -1)^2 -9 +121 =0

16(x-4)^1 +9(y -1)^2 = 144

(x-4)^1/9 + (y-1)^2/16 =1

(h, k) = ( 4 , 1)

a = 3 ; b = 4