G. For all \theta in the range 0 \leq \theta

Correct Answer is : two values of θ

Oxford University MAT 2017 Solved Papers

Question : 7 of 10

Marks: +1, -0

G. For all

θ

in the range

0 ≤ θ< 2 π

the line

(y-1) \cos θ=(x+1) \sin θ

divides the disc

x^2+y^2 ≤ 4

into two regions. Let

A(θ)

denote the area of the larger region.
Then

A(θ)

achieves its maximum value at

Solution:

For

θ=0

, the line is simply

y=1

. Adjusting

θ

alters the gradient of the line, pivoting around the point

(-1,1)

(as shown in the diagram below). By symmetry this shows that there are two possible values to maximise

A(θ)

and so the answer is (b).

Go to Question:

Prev Question

Next Question