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an ellipse is represented using the equation . where are the foci of the ellipse located? check all that apply.
(−29, 7)
(19, 7)
(−21, 7)
(13, 7)
(−5, −17)
(−5, 31)
equation:

Options A and B.

Step-by-step explanation:

An ellipse is represented by the equation

We have to find the foci of the given ellipse.

Ellipse having equation

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.

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step-by-step explanation: