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Solution for Find the Centre and Radius of the Circle X2 + Y2 – 4x – 8y – 45 = 0 - CBSE (Arts) Class 11 - Mathematics

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Question

Find the centre and radius of the circle x2 + y2 – 4x – 8y – 45 = 0

Solution

The equation of the given circle is x2 + y2 – 4x – 8y – 45 = 0.

x2 + y2 – 4x – 8y – 45 = 0

⇒ (x2 – 4x) + (y– 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 = `(sqrt(65))^2`, which is of the form (x – h)2 + (y – k)2 = r2, where h = 2, k = 4, and `r = sqrt65`.

Thus, the centre of the given circle is (2, 4), while its radius is `sqrt65`

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Solution Find the Centre and Radius of the Circle X2 + Y2 – 4x – 8y – 45 = 0 Concept: Concept of Circle.
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