Given the equation 4x^2 + 4y^2 = 4, we can rewrite it as x^2 + y^2 = 1, which is the equation for a circle with a radius of 1 centered at the origin (0,0).
Since the equation shows symmetry about both the x-axis and the y-axis, we can use this symmetry to find more points on the graph.
For example, if we substitute x = 2 and y = 0 into the equation, we get:
(2)^2 + (0)^2 = 1
4 + 0 = 1
4 = 1
This shows that the point (2,0) is not on the graph of the circle.
However, we can use the symmetry to find the point (-2, 0) as a point on the graph.
Substitute x = -2 and y = 0 into the equation:
(-2)^2 + (0)^2 = 1
4 = 1
Since 4 does not equal 1, the point (-2,0) is not on the graph.
Therefore, the graph of the equation x^2 + y^2 = 1 contains the points (0,1), (0,-1), (1,0), and (-1,0) due to symmetry.
(2,0):4x*2+4y*2=4
use symmetry to find at least one more point on the graph
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