A lesson in why to draw pictures


Everyone had trouble with question 6b(ii) of the FP1 “withdrawn” paper of June 2013. “A curve C is in the form of a parabola with equation y2=4x. P(p2, 2p) and Q(q2, 2q) are points on C where p>q. (a) Find an equation of the tangent to C at P. (b) The tangent at P and the tangent at Q are perpendicular and intersect at the point R(–1, 2). (i) Find the exact value of p and the exact value of q. (ii) Find the area of the triangle PQR“.

Drawing a picture makes it much easier. From part (b)(i), p=1+√2 and q+1-√2, so P is (3+2√2, 2+2√2) and Q is (3−2√2, 2−2√2)


So, if I have two words of advice for you, they are:

Draw diagrams

If I have nine words, they are:

Draw big, clear diagrams, labelled with all your information

If I have twelve words, they are:

Draw big, clear diagrams, with a ruler, labelled with all your information.

(An experimental study calculated that in fact on average a picture is worth 84.1 words. Terry Tao’s version of the adage is: a picture is worth a thousand equations).