5 The diagram shows the hyperbola
$$\frac { x ^ { 2 } } { 4 } - y ^ { 2 } = 1$$
and its asymptotes.
\includegraphics[max width=\textwidth, alt={}, center]{a0a30197-ca11-40d9-9ccd-30281c5e0fb4-03_531_1013_616_516}
- Write down the equations of the two asymptotes.
- The points on the hyperbola for which \(x = 4\) are denoted by \(A\) and \(B\).
Find, in surd form, the \(y\)-coordinates of \(A\) and \(B\).
- The hyperbola and its asymptotes are translated by two units in the positive \(y\) direction.
Write down:
- the \(y\)-coordinates of the image points of \(A\) and \(B\) under this translation;
- the equations of the hyperbola and the asymptotes after the translation.