Find the equation of the hyperbola whose: focus is at (5,2) vertex at (4,2) and centre  at (3,2)

Explanation

Let `(x_2,y_2)` be the coordinates of the second vertex

We know that the centre of the hyperbola is the mid-point of the line-joining the two vertices.

`(x_1+4)/2=3` and `(y_1+2)/2=2`

[Centre=`(3,2)` and vertex=`(4,2)`]

`impliesx_1=2 `and` y_2=2`

The coordinates of the second vertex is (2,2)

Let `2a` and `2b` the length of gransvers and conjugate axes and let e be eccentreicity. Then the equation of hyperbola is

`(x−3)^2/a^2−(y−2)^2/b^2=1...(i)`

...