Find an equation of the ellipse with center at the origin that passes through the points(1, -10√2/3) and (-2, 5√5/3).

It's a homework problem I have been so stuck on.

Can someone help, please?

Thanks

Let its equation be (x^2/a^2) + (y^2/b^2) = 1 ;

since, it passes through (1, - 10√2/3), therefore,

(1/a^2) + (22.22/b^2) = 1 ;

(1/a^2) = 1 - (22.22/b^2) ;

1/a^2 = (b^2 - 22.22)/b^2 ;


It passes through (- 2, 5√5/3), then

4/a^2 + (13.89/b^2) = 1 ;

4(b^2 - 22.22)/b^2 + (13.89/b^2) = 1 ;

(4b^2 - 88.88 + 13.89) = b^2 ;

3b^2 = 74.89 ;

b^2 = 24.99 (approximated to 25) .

a^2 = b^2 / (b^2 - 22.22) = 25 /(25 - 22.22) = 8.99 (approximated to 9).

The equation is (x^2/9) + (y^2/25) = 1 .