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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