Area of ellipse = πab

a: length of semi-major axis (half the length of the major axis)

b: length of semi-minor axis (half the length of the minor axis)

Re-write the ellipse in standard form first:

9x^2-36x+25y^2=189

@ y = 0,

9x^2-36x+25y^2 -189 = 0 

--> 9x^2 - 36x = 189

--> x ^2 - 4x - 21 = 0

-->(x - 7)(x + 3) = 0 --> x = 7, x = -3

@ x = 0

9x^2-36x+25y^2 - 189 = 0

--> 25y^2 = 189 --> y = + or - sqrt(189/25) = 3 --> y = 3, y = -3

This gives a = 7 and b = 3. Thus, the area is:

A = πab = π(7)(3) = 21π square units.