The points are (3, 1) and (3 + 4t, 1 + 3t).

Slope formula: $\"\"$

The equation of hyperbola is $\"\"$ .

So, the center of hyperbola is $\"\"$ and a = 3, b = 5.

The transverse axis parallel to the x - axis.

The vertices are $\"\"$ .

The relation between a, b and c is $\"\"$ for hyperbola.

$\"\"$ (Substitute $\"\"$ )

$\"\"$ (Simplify)

The foci of hyperbola are $\"\"$ .

The center of hyperbola is $\"\"$ , vertices are $\"\"$ and its foci are

$\"\"$