Define a unit circle and prove that any point $(x, y)$ on the unit circle satisfies the equation $x^2 + y^2 = 1$.
Answer 1
Mia Harris
A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) in the Cartesian coordinate system.
To prove that any point $ (x, y) $ on the unit circle satisfies $ x^2 + y^2 = 1 $, we start with the definition of a circle:
$ (x – h)^2 + (y – k)^2 = r^2 $
For a unit circle, the center is at (0, 0) and the radius $ r $ is 1, so the equation becomes:
$ x^2 + y^2 = 1 $
Thus, any point $ (x, y) $ on the unit circle will satisfy this equation.
Answer 2
Samuel Scott
A unit circle is defined as a circle with a radius of 1 and centered at the origin (0,0).
Given the general equation of a circle:
$ (x – h)^2 + (y – k)^2 = r^2 $
For a unit circle:
$ (x – 0)^2 + (y – 0)^2 = 1^2 $
This simplifies to:
$ x^2 + y^2 = 1 $
Therefore, any point (x, y) on the unit circle satisfies the equation $ x^2 + y^2 = 1 $.
Answer 3
Lucas Brown
A unit circle is a circle with radius 1 centered at the origin.
Its equation is:
$ x^2 + y^2 = 1 $
Any point (x, y) satisfies this equation.
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