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Question
Answer the following :
Find the centre and radius of the circle x = 3 – 4 sinθ, y = 2 – 4cosθ
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Solution
Given, x = 3 – 4 sinθ, y = 2 – 4cosθ
∴ x – 3 –4 sinθ, y –2 = – 4cosθ
On squaring and adding, we get
(x – 3)2 + (y – 2)2 = (–4 sinθ)2 + (–4 cosθ)2
∴ (x – 3)2 + (y – 2)2 = 16sin2θ + 16cos2θ
∴ (x – 3)2 + (y – 2)2 = 16(sin2θ + cos2θ)
∴ (x – 3)2 + (y – 2)2 = 16(1)
∴ (x – 3)2 + (y – 2)2 = 16
∴ (x – 3)2 + (y – 2)2 = 42
Comparing this equation with
(x – h)2 + (y – k)2 = r2, we get
h = 3, k = 2, r = 4
∴ Centre of the circle is (3, 2) and radius is 4.
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