What is the type of conic section given by the equation x^2 - 9y^2 = 900 and what is the domain and range?
show the work if you can.

A conic section is a curve obtained by the intersection of the surface of a cone with a plane. A conic section can be a circle, a hyperbola, a parabola, and an ellipse.

For a circle, the general equation of a circle with center, (a, b), and a radius, r, is of the form


For a hyperbola, the general equation of a hyperbola with center (h, k), and a and b half the lengths of the major and the minor axis respectively is of the form.


For a parabola, the general equation of a parabola with center (h, k), and a multiplier a is of the form


For an ellipse, the general equation of an ellipse with center (h, k), and a and b half the lengths of the major and the minor axis respectively.


Given the equation

It can be rewritten as

This gives an equation of a hyperbola with center (0, 0), half the length of the major axis = 30 and half the length of the minor segment = 10.

The domain of the equation is all real values of x.