Pearson Edexcel IAL Mathematics FP1.4.3 Focus-directrix property of the parabola

Practise using the focus-directrix property of parabolas to form distances, line intersections, exact lengths and triangle areas.

Exam points

find the focus or directrix from y^2=4ax before calculating a length or area
use equal distance to focus and directrix to derive PS or locate a point
combine directrix intersections with triangle area ratios to solve for a constant

[Maximum number: 1]

The parabola C has equation $y^{2}=20 x$

The point P on C has coordinates ( $5 p^{2}, 10 p$ ) where p is a non-zero constant.

The point S is the focus of C. Write down the coordinates of S.

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