, 9x^2 + 16y^2 - 18x + 64y = 71.

 To change the expressions into a perfect square trinomial add (half the x coefficient)² to each side of the expression

 Here x coefficient = 2. so, (half the x coefficient)² = (2/2)²= 1

and y coefficient = 4. so, (half the y coefficient)² = (4/2)²= 4.

Add 9(1) and 16(4) = 64 to each side.

To find the foci, substitute the values of a = 4 and b = 3 in the equation .

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Center (h, k) = (1, -2)