Identify the center of the ellipse with equation x^2+2y^2-10x+8y+25=0

(5, -2)

Step-by-step explanation:

The equation of the ellipse is given by:

where is the center of the ellipse.

The given equation of the ellipse is:

x² + 2y² - 10x + 8y + 25 = 0.

We have to reduce to the standard form so that we can compare and determine the center of the ellipse.

Subtracting from the equation on both sides, we get:

x² - 10x + 2y² + 8y + 25 - 25 = - 25

The next step would be complete the squares. Let us complete first.

Now for .

Therefore the equation becomes:

(x - 5)² + 2(y + 2)² = -25 + 25 + 8

⇒ (x - 5)² + 2(y - 2)² = 8

Since the needs 1, we divide the entire equation by 8.

⇒

Comparing with standard form we get:

and

⇒ (h,k) = (5,-2)

∴ The center of the ellipse is (5,-2).

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step-by-step explanation: