EXAMPLE 1: Find the center and radius of a circle
(x – 1)² + (y – 4)² = 16
SOLUTION:
The standard equation of a circle is:
(x – h)² + (y – k)² = r²
where (h, k) is the center of a circle and r is the radius of a circle.
Compare the given equation with the standard equation of a circle.
we get
h = 1
k = 4
So, center of a given circle = (h, k) = (1, 4)
and
r² = 16
⇒ either r = +4 or r = – 4 (By taking square root on both sides)
Since r is the length and length cannot be negative, so radius r of a given circle is 4.
Thus, the circle whose equation is (x – 1)² + (y – 4)² = 16 has center at (1, 4) and its radius is 4.
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