Symmetry Circles Graphing Key Equations What is Symmetry

Symmetry & Circles Graphing Key Equations

What is Symmetry? Symmetry

Symmetry with Respect to x-Axis If the graph contains the point (x, y), then must contain the point (x, -y). Remember that you are folding it over a horizontal line therefore the y value is changing (folding down).

Symmetry with Respect to y-axis If the graph contains the point (x, y), then it must also contain the point (-x, y). Remember you are folding it over a vertical line, therefore the x is going to change (folding one side over the other).

Symmetry with Respect to the Origin If the graph contains the point (x, y), then it must also contain the point (-x, -y). Remember, you are folding the graph both horizontally and vertically. This changes both the x and y values.

Testing for Symmetry X-Axis: Replace y by –y in equation. (Will only be true if there is a y^2 somewhere in the equation. Y-Axis: Replace x by –x in the equation. Origin: Replace x by –x and y by –y.

Circles Definition of Circle

Circles Earth is represented on a map of the solar system so that its surface is the circle with equation x^2+y^2 +2 x +4 y -4091 = 0. What does this all mean?

Equation of a Circle How to find the equations of a circle.

Circles Write an equation for the path of a communications satellite in a circular orbit 22, 000 miles above the earth. (Assume that the radius of the earth is 4000 miles. ) How would this equation change if the orbit is 30, 000 miles above the earth?