FP1 January 2010 Q4

EdexcelOld spec6 marksConic Sections

4.

Figure 1: parabola y squared = 12x with focus S on the x-axis, dashed directrix through A on the x-axis, and horizontal line from B on the directrix to P on the parabola, P joined to S
Figure 1

Figure 1 shows a sketch of part of the parabola with equation \(y^2 = 12x\).

The point \(P\) on the parabola has \(x\)-coordinate \(\dfrac{1}{3}\).

The point \(S\) is the focus of the parabola.

(a) Write down the coordinates of \(S\). (1)

The points \(A\) and \(B\) lie on the directrix of the parabola.
The point \(A\) is on the \(x\)-axis and the \(y\)-coordinate of \(B\) is positive.

Given that \(ABPS\) is a trapezium,

(b) calculate the perimeter of \(ABPS\). (5)
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