Find an equation of the hyperbola such that for any point on

Find an equation of the hyperbola such that for any point on the hyperbola, the difference between its distances from the points (5, 1) and (11, 1) is 4.

Solution

h =(5+11)/2 =8 ; k = (1 +1)/2= 1----> ( 8, 1)Stad equation of hyperbola with (h,k) as vertices:

(x -h)^2/a^2 +(y-k)^2/b^2 =1

= 2a = 4 ----> a =2

We can find b from realtion : a^2 +b^2 = c^2

b^2 = 6^2 -2^2 = 36 -4 = 32

So,Equation of Hyeperbola :

(x -8)^2/4 +(y-1)^2/32 =1