Graph a Hyperbola with vertices(2,4),(8,4), foci(-2,4), (12,4), center(5,4). Can someone help me find the equation for this?

1 Answer
Mar 15, 2018

generalize form of equation of hyperbola is #(x-h)^2/a^2 - (y-k)^2/b^2=1#

Where,#(h,k)# is the coordinate of the centre,

and, #a# is distance between the centre and the vertices,and #c# is the distance between the centre and the focus.

and, #a^2 +b^2=c^2#

So,given, #(h,k)=(5,4)#

#a= sqrt((5-2)^2 +(4-4)^2)=3#

#c=sqrt((5-12)^2 +(4-4)^2)=7#

so,#b^2=(7^2-3^2)=40#

So,the equation of the hyperbola becomes, #(x-5)^2/9 - (y-4)^2/40 =1#

Now,see the graph below

graph{((x-5)^2)/9 - ((y-4)^2)/40=1 [-20, 20, -10, 10]}