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A-Level MathematicsYear 2022Q1

2   1. An ellipse has equation x y 2 2 16 4 1 and eccentricity e 1 A hyperbola has equation x a y b 2 2 2 2 1 and eccentricity e 2 Given that e 1 × e 2 = 1 (a) show that a 2 = 3b 2 (4) Given also that the coordinates of the foci of the ellipse are the same as the coordinates of the foci of the hyperbola, (b) determine the equation of the hyperbola. (3) ___________________________________________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Turn over 3   Question 1 continued _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___________________________________________ (Total for Question 1 is 7 marks)

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)