Find the centre and radius of the circle x 2 + y 2 – 8x + 10y – 12 = 0
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
,
which is of the form (x – h)2 + (y
– k)2 = r2, where h
= 4, k = –5, and
.
Thus, the centre of the
given circle is (4, –5), while its radius is
.