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

1.	Find the centre and radius of the circle x2 + y2 – 4x – 8y – 45 = 0
Answer» The equation of the given circle is 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 ⇒ ( – 2)² + ( –4)²= √65 , Which is of the form (x – h)² + (y – k)² = r², where h = 2, k = 4 and = √65 , Thus, the centre of the given circle is (2, 4), while its radius is √65 .

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