Question

Which equation represents the hyperbola (y -2)^2/4 - (x-2)^2/9=1
in general form?

Answer 1

`9y^2-4x^2-36y+16x-16=0`

Explanation:

The given hyperbola has equation:

`((y-2)^2)/(4)-((x-2)^2)/(9)=1`

We multiply through by 36 to get:

`9(y-2)^2-4(x-2)^2=36`

We expand to get:

`9(y^2-4y+4)-4(x^2-4x+4)=36`

`9y^2-36y+36-4x^2+16x-16=36`

`9y^2-36y-4x^2+16x-16=0`

The equation of the hyperbola in general form is:

`9y^2-4x^2-36y+16x-16=0`