7 A hyperbola \(H\) has equation
$$\frac { x ^ { 2 } } { 9 } - y ^ { 2 } = 1$$
- Find the equations of the asymptotes of \(H\).
- The asymptotes of \(H\) are shown in the diagram opposite. On the same diagram, sketch the hyperbola \(H\). Indicate on your sketch the coordinates of the points of intersection of \(H\) with the coordinate axes.
- The hyperbola \(H\) is now translated by the vector \(\left[ \begin{array} { r } - 3
0 \end{array} \right]\).
- Write down the equation of the translated curve.
- Calculate the coordinates of the two points of intersection of the translated curve with the line \(y = x\).
- From your answers to part (c)(ii), deduce the coordinates of the points of intersection of the original hyperbola \(H\) with the line \(y = x - 3\).
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