How do you find the center, foci and vertices of the hyperbola #(x-1)^2/4-(y+2)^2/1=1#?

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Answer 1 · 2018-04-21T20:01:51

please check the explanation below

consider the equation to be:

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

is an equation of a horizontal hyperbola

#a=2# #" , "##b=1#

#b^2=a^2(e^2-1)##rarr# #e=sqrt5/2#

it's center is #(h,k)rarr(1,-2)#

it's foci are #(h+-ae,k)rarr(1+-sqrt5,-2)#

its vertices are #(h+-a,k)rarr(1+-2,-2)#