- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The rectangular hyperbola \(H\) has equation \(x y = 20\)
The point \(P \left( 2 t \sqrt { a } , \frac { 2 \sqrt { a } } { t } \right) , t \neq 0\), where \(a\) is a constant, is a general point on \(H\)
- State the value of \(a\)
- Show that the normal to \(H\) at the point \(P\) has equation
$$t y - t ^ { 3 } x - 2 \sqrt { 5 } \left( 1 - t ^ { 4 } \right) = 0$$
The points \(A\) and \(B\) lie on \(H\)
The point \(A\) has parameter \(t = c\) and the point \(B\) has parameter \(t = - \frac { 1 } { 2 c }\), where \(c\) is a constant.
The normal to \(H\) at \(A\) meets \(H\) again at \(B\) - Determine the possible values of \(C\)