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

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Answer 1 · 2015-06-22T21:07:52

It is an equation of a hyperbola

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

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