Question 564980
Hi, the equation of a hyperbola is
{{{(X^2)/(a^2)-(Y^2)/(b^2)=1}}}
So, consider the left hand side of the equation given in the problem.  We can complete the square by adding 9 to both sides.  This gives us:
{{{9(y+1)^2=25x^2+225}}}
Rearranging, and letting X=x, Y=y+1, we get:
{{{(X^2)/(225/25)-(Y^2)/(225/9)=1}}}
This is the equation of a hyperbola for say z and w:
{{{(z^2)/(225/25)-(w^2)/(225/9)=1}}}
Shifted one unit down (we would need to take w=y+1 to get the equation given in X,Y)