2013澳大利亚高考数学试题答案(16)

Question 16 (continued)

(i) What information indicates that P lies on an ellipse with foci S and S′,

and with eccentricity e? (ii) Using the focus–directrix definition of an ellipse, or otherwise, show that

SP = a(1 e cosθ ).

(iii) Show that sin β =

e + cos θ

1 + ecos .

(iv) By considering the forces acting on P in the vertical direction, show that

2T mg1 e 2

=

cosθ

1 e 2 cos 2

θ

.

(v) Show that the force acting on P in the horizontal direction is

mrω 2 =

2T 1 e2 sin θ

1 e 2 cos 2

θ

.

tanθ =(vi)

Show that End of paper

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