Question

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?

Answer 1

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]}