A-Level MathematicsYear 2020Q7
20 7. The points P(9p2, 18p) and Q(9q2, 18q) , p ≠ q , lie on the parabola C with equation y2 = 36x The line l passes through the points P and Q (a) Show that an equation for the line l is ( p + q) y = 2(x + 9pq) (3) The normal to C at P and the normal to C at Q meet at the point A. (b) Show that the coordinates of A are (9( p2 + q2 + pq + 2) , −9pq( p + q)) (7) Given that the points P and Q vary such that l always passes through the point (12, 0) (c) find, in the form y2 = f ( x ) , an equation for the locus of A, giving f ( x ) in simplest form. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9FM0_3A_que_20201016.pdf
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Exam Specification Info
This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.
Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)