How do you classify #x^2-y^2-4x-3=0#?

1 Answer
Jun 22, 2015

Answer:

It is an equation of a hyperbola

Explanation:

The equation contains #x^2# and #y^2# so it may be:

  1. Circle or elypse
  2. Hyperbola

But the sign of #y^2# is negative, so it cannot be an elipse or circle.

You can also check if it is possible to transform the eqation to form:

#x^2/a^2-y^2/b^2=1# #(1)#

#x^2-y^2-4x-3=0#

#x^2-4x color(red)(+4) color(red)(-4)-3-y^2=0#

#(x-2)^2-y^2=7#

#(x-2)^2/7-y^2/7=1#

So this equation is in the form (1) which prooves it is a hyperbola