$ ext{Find the equation of a unit circle}$
Answer 1
Christopher Garcia
To find the equation of a unit circle centered at the origin, we need to remember that a unit circle has a radius of 1. The standard form of a circle’s equation is:
$ (x – h)^2 + (y – k)^2 = r^2 $
Where (h, k) is the center of the circle and r is the radius. Since the unit circle is centered at the origin (0, 0) and has a radius of 1, we can plug in these values:
$ (x – 0)^2 + (y – 0)^2 = 1^2 $
Simplifying this, we get:
$ x^2 + y^2 = 1 $
The equation of the unit circle is:
$ x^2 + y^2 = 1 $
Answer 2
Matthew Carter
The equation of a unit circle is derived from the general circle equation:
$ (x – h)^2 + (y – k)^2 = r^2 $
For a unit circle, the radius r is 1, and the center is at the origin (0, 0). Thus, we substitute h = 0, k = 0, and r = 1:
$ (x – 0)^2 + (y – 0)^2 = 1^2 $
Which simplifies to:
$ x^2 + y^2 = 1 $
Therefore, the equation of the unit circle is:
$ x^2 + y^2 = 1 $
Answer 3
Alex Thompson
The unit circle’s equation can be written as:
$ x^2 + y^2 = 1 $
This is because the center is at (0, 0) and the radius is 1.
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