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Question
Find the equation of the circle whose centre is (-3, -2) and having circumference 16π.
Solution
Circumference, 2πr = 16π
⇒ 2r = 16
⇒ r = 8
Equation of the circle when centre and radius are known is (x – h)2 + (y – k)2 = r2
⇒ (x + 3)2 + (y + 2)2 = 82
⇒ x2 + 6x + 9 + y2 + 4y + 4 = 64
⇒ x2 + y2 + 6x + 4y + 13 = 64
⇒ x2 + y2 + 6x + 4y – 51 = 0
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