How do you find the standard form of the equation of the hyperbola given the properties vertex (0,1), vertex (8,1), focus (-3,1)?

1 Answer
Aug 1, 2017

Answer:

#(x-4)^2/16-(y-1)^2/33=1#

Explanation:

As the two vertex are #(0,1)# and #(8,1)# and focus is #(-3,1)#

as the distance between #(0,1)# and #(-3,1)# is #3#, the other focus is #(11,1)# (at a distance of #3# to the right of #(8,1)#) and central point is #(4,1)#.

Hence, #a=4#, the distance to either side of center and #c=7#, the distance from center to focus.

Hence, #b^2=c^2-a^2=33#

and equation is

#(x-4)^2/16-(y-1)^2/33=1#

graph{((x-4)^2/16-(y-1)^2/33-1)((x+3)^2+(y-1)^2-0.03)((x-11)^2+(y-1)^2-0.03)((x-4)^2+(y-1)^2-0.03)(x^2+(y-1)^2-0.03)((x-8)^2+(y-1)^2-0.03)=0 [-6, 14, -4.5, 5.5]}