Find an equation for the hyperbola described Center at 28 fo

Find an equation for the hyperbola described. Center at (2,8) focus at (-5,8) vertex at (1,8)

Solution

The given hyperbola is of the form

(x-h)²/a² - (y-k)²/b²=1

where centre is (h,k)

vertices are (h+a,k) and (h-a,k)

focii are (h+c,k),(h-c,k)

In the given question centre is (2,8)

Therefore h=2 ,k=8

vertex =(1,8)

h-a=1

2-a=1

a=1

focii is at (-5,8)

h-c=-5

2-c=-5

c=7

c²=a² + b²

49=1+b²

b=sqrt48

Therefore required equation is (x-2)²/1 +(y-8)²/48=1