Find the center foci right and left and verticles right and

Find the center, foci (right and left), and verticles (right and left) of the eclipse. Graph the equation.

9x^2 + 16y^2 - 90x + 32y + 97 = 0

Please explain how to do this. I keep getting it wrong.

Thank you!

Find the center, foci (right and left), and verticles (right and left) of the eclipse. Graph the equation.

9x^2 + 16y^2 - 90x + 32y + 97 = 0

Please explain how to do this. I keep getting it wrong.

Thank you!

9x^2 + 16y^2 - 90x + 32y + 97 = 0

Please explain how to do this. I keep getting it wrong.

Thank you!

9x²+16y²-90x +32y +97=0

9(x²-10x) +16(y²+2y)+97=0

9(x²-10x +25 -25)+16(y²+2y +1-1) +97=0

9(x-5)²+16(y+1)² -225 -16+97=0

9(x-5)²+16(y+1)²=144

(x-5)²/16 + (y+1)²/9 =1

This is of the form

(x-h)²/a² + (y-k)²/b² =1

Centre is (h,k) that is (5,-1)

vertices (h+-a,k) = (5+-4,-1) = (9,-1),(1,-1)

focii= (h+-c,k)

c=sqrt(a²-b²) = sqrt7

focii (5+-sqrt7,-1)