Describe a geometrical transformation by which the hyperbola
$$x ^ { 2 } - 4 y ^ { 2 } = 1$$
can be obtained from the hyperbola \(x ^ { 2 } - y ^ { 2 } = 1\).
The diagram shows the hyperbola \(H\) with equation
$$x ^ { 2 } - y ^ { 2 } - 4 x + 3 = 0$$
By completing the square, describe a geometrical transformation by which the hyperbola \(H\) can be obtained from the hyperbola \(x ^ { 2 } - y ^ { 2 } = 1\).