(2,0):4x*2+4y*2=4

use symmetry to find at least one more point on the graph

1 answer

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.