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Rates of change and differential equations — Question 279

Original QCE Vault practice · 6 marks

Q279 · Practice questionTechnology-freeSimple familiar6 marks

QUESTION 279 (6 marks)

An ellipse has equation x2/9+y2/4=1x^2/9+y^2/4=1. Point P on its upper half has coordinates (33/2,1)(3\sqrt3/2,1).
Question 132 stimulus; see the question for exact data and required construction.
a)
Use implicit differentiation to determine dy/dxdy/dx and its value at P.
[2 marks]
b)
Determine a Cartesian equation of the tangent at P.
[2 marks]
c)
Sketch the ellipse and the tangent on the blank axes. Label all axis intercepts of both.
[2 marks]
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