How do you write the equation of the hyperbola given Foci: (-4,0),(4,0) and vertices (-1,0), (1,0)?

Question

5179 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-15T09:29:38

#x^2-y^2/15=1#

As focii #(-4,0)#, #(4,0)# and vertices #(-1,0)#, #(1,0)# lie on the same line #y=0#, i.e. #x#-axis,

Further, as the mid point of vertices is #(0,0)#, the equation i of the type

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

As the distance between focii is #8# and between vertices is #2#,

we have #c=8/2=4# and #a=2/2=1#

and hence as #c^2=a^2+b^2#, #b=sqrt(4^2-1^2)=sqrt15#

and equation of hyperbola is

#x^2/1-y^2/15=1# or #15x^2-y^2=15#
graph{15x^2-y^2-15=0 [-10, 10, -5, 5]}