What is the Standard Equation of a Circle?
CIRCLE:
If (h, k) is a fixed point in the plane, then the circle of radius r centered at (h, k) is defined as the set of all points in the plane whose distance from (h, k) is r
The standard equation of a circle is:
(x – h)² + (y – k)² = r² ————————(1)
The standard equation of a circle can be used to find an equation of a circle if its radius and co-ordinates of its center are given.
Also, if the equation of a circle is given, we can find its radius and co-ordinates of its center by comparing it with the standard equation of a circle.
UNIT CIRCLE:
Consider a circle whose center is at origin, that is,
(h, k) = (0, 0)
and has radius 1.
Then, its equation can be found from equation (1) by putting
h = 0,
k = 0 and
r = 1
(x – 0)² + (y – 0)² = 1²
x² + y² = 1
Such a circle is called a unit circle.
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