Answer:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
Step-by-step explanation:
The given hyperbola has equation:
[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]
We multiply through by 36 to get:
[tex]9(y-2)^2-4(x-2)^2=36[/tex]
We expand to get:
[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]
[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]
[tex]9y^2-36y-4x^2+16x-16=0[/tex]
The equation of the hyperbola in general form is:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
