FP1 June 2013 (R) Q5

EdexcelOld spec8 marksConic Sections

5.

Figure 1: the rectangular hyperbola H with branches in the first and third quadrants, and the line L crossing H at P in the first quadrant and at Q in the third quadrant
Figure 1

Figure 1 shows a rectangular hyperbola \(H\) with parametric equations \[x = 3t, \quad y = \frac{3}{t}, \quad t \neq 0\]

The line \(L\) with equation \(6y = 4x - 15\) intersects \(H\) at the point \(P\) and at the point \(Q\) as shown in Figure 1.

(a) Show that \(L\) intersects \(H\) where \(4t^2 - 5t - 6 = 0\) (3)
(b) Hence, or otherwise, find the coordinates of points \(P\) and \(Q\). (5)
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