Question
(2,0):4x*2+4y*2=4
use symmetry to find at least one more point on the graph
use symmetry to find at least one more point on the graph
Answers
GPT 3.5
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.
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.