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Answer on Analytic Geometry Question for liz perez

Question #6869
x^2-9y^2+36y-45=0
Expert's answer
x^2-9y^2+36y-45=0
x^2-(9y^2-36y+36)-45+36=0
x^2-(3y-6)^2-9=0
x^2-9(y-2)^2=9
x^2/9-(y-2)^2=1 we have equation of hyperbola here
In general case an east-west opening hyperbola centered at (h,k) has the equation
<img style="width: 153px; height: 43px;" src="data:image/png;base64,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" alt="">
So in our task we have hyperbola centered at (0,2), also we have a=9, b=1
<img style="width: 425px; height: 421px;" src="data:image/png;base64,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" 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