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]}