Question 430947
Solution: The center of this ellipse is the point (1, -2), a^2=25 and b^2=16

As we know c^2=a^2-b^2=25-16=9, thus, {{{c^2=9}}}, And c=/- sqrt(9)

c=-3 and c=3, hence the coordinates of the foci will be:(-3,0) and (3,0),when the  ellipse was centered at (0, 0), Our ellipse was shifted at poit (1, -2), thus the new foci will be:(-3+1, 0-2) and (3+1, 0-2), simplify: (-2, -2) and (4, -2).

Answer: the foci of ellipse are: (-2, -2) and (4, -2)

{{{drawing(400, 300, -10, 10, -10, 10, grid(1), blue ( ellipse (1, -2, 10, 8)))}}}

Done.