Answer:
Options A and B.
Step-by-step explanation:
An ellipse is represented by the equation [tex]\frac{(x+5)^{2}}{625}+\frac{(y-7)^{2}}{49}=1[/tex]
We have to find the foci of the given ellipse.
Ellipse having equation [tex]\frac{(x-h)^{2}}{a^{2} }+ \frac{(y-k)^{2} }{b^{2} }=1[/tex]
Then center of this ellipse is represented by (h, k) and foci as (c, 0) and (-c, 0).
And c is represented by c² = a² - b²
So we co relate this equation with our equation given in the question.
a = √625 = 25
b = √49 = 7
and c² = (25)² - (7)²
c² = 625 - 49 = 576
c = ±√576
c = ±24
Now we know center of the ellipse is at (-5, 7) so foci can be obtained by adding and subtracting x = 24 from the coordinates of the center.
Center 1 will be [(-5+24=19), 7] ≈ (19, 7)
Center 2 will be [(-5-24=-29), 7] ≈ (-29, 7)
Therefore, options A and B are correct.
