Verified answer

x^2 - y^2 + 9 = 0

Subtract 9:

x^2 - y^2 = -9

Divide through by -9:

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

-x^2/9 + y^2/9 = 1

Now swap the variables round

y^2/9 - x^2/9 = 1

So a^2 = b^2 = 9, or a = b = 3. Note that it doesn't matter really which way round x and y are; it will just affect the orientation of the hyperbola (which direction it points in).

it is a hyperbola .

x^2 - y^2 =-9.

divide both sides by 9

x^2/9 - y^2/9 = -1

a=b=3.......it is rectangular conjugate hyperbola.