Question

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

Answer 1

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 .