Question

Find the centre and radius of the circle x² + y² – 8x + 10y – 12 = 0

Answer 1

The equation of the given circle is x² + y² – 8x + 10y – 12 = 0.
x² + y² – 8x + 10y – 12 = 0
⇒ (x² – 8x) + (y² + 10y) = 12
⇒ {x² – 2(x)(4) + 4²} + {y² + 2(y)(5) + 5²}– 16 – 25 = 12
⇒ (x – 4)² + (y + 5)2 = 5³

 ⟹(−4)²+{−(−5)}²=(√53)²
which is of the form (x – h)² + (y – k)² = r², where h = 4, k = – 5 and r = √53
Thus, the centre of the given circle is (4, –5), while its radius is √53.