find the centre and radius of the circle whose equation is given by x2+y2-4x-8y-45=0
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Given equation: x2 + y2 – 4x – 8y – 45 = 0.
x2 + y2 – 4x – 8y – 45 = 0
(x2 – 4x) + (y2 -8y) = 45
(x2 – 2(x) (2) + 22) + (y2 – 2(y) (4) + 42) – 4 – 16 = 45
(x – 2)2 + (y – 4)2 = 65
(x – 2)2 + (y – 4)2 = (√65)2
The equation is of the form (x-h)2 +(y-k)2 = r2 ,where h = 2, k = 4 and r = √65
Therefore, the centre is (2, 4) and its radius is √65.
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