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A-Level MathematicsYear 2022Q5

12   5. The rectangular hyperbola H has equation xy = 36 (a) Use calculus to show that the equation of the tangent to H at the point P 6 6 t t , is yt 2 + x = 12t (3) The point Q t t 12 3 , also lies on H. (b) Find the equation of the tangent to H at the point Q. (2) The tangent at P and the tangent at Q meet at the point R. (c) Show that as t varies the locus of R is also a rectangular hyperbola. (4) ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 13   Question 5 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________

Paper Source:9fm0-3a-que-20220616.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)