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Answer:
[tex]\frac{(x-3)^2}{4^2} +\frac{(y-1)^2}{6^2} =1[/tex]
Step-by-step explanation:
[tex]9x^{2}+4y^{2} -54x-8y-59=0[/tex]
[tex]9x^{2}-54x+4y^{2} -8y=59[/tex]
Factor 9 and 4 out
[tex]9(x^2-6x)+4(y^2-2y)=59[/tex]
Complete the square, don't forget to add the 2 extra numbers
[tex]9(x-3)^2+4(y-1)^2=59+81+4[/tex]
[tex]9(x-3)^2+4(y-1)^2=144\\[/tex]
Divide everything by 144
[tex]\frac{(x-3)^2}{16} +\frac{(y-1)^2}{36} =1[/tex]