Question

what is the type of conic section is given by the equation x^2-9y^2=900 an waht is the domain and range?

Answer 1

When the squared terms are of different signs, the equation generally describes a hyperbola. This one has its vertices at x=±30, so the parameters of interest are
  domain: (-∞, -30] ∪ [30, ∞)
  range: (-∞, ∞)