Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The given hyperbola has equation:

$\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1$

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:

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