Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.
Now,
it's vertex is given, I.e (7 , -5)
so, length of semi transverse axis will be equal to distance of vertex from centre, i.e
- a = 7 - 3 = 4 units
Now, it's focus can be represented as ;
so,
- ae + 3 = 9
and we know, a = 4
Now, let's find the measure of semi - conjugate axis (b)
So, it's time to write the equation of hyperbola, as we already have the values of a and b ~
[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]