HPC 1.3 Notes Learning Targets: - Test an equation for symmetry with respect to: x-axis, y-axis, or origin - Know how to graph key equations - Write the standard form of the equation of a circle - Graph a circle by hand and with your calculator - Find the center and radius of a circle from an equation in general form

Symmetry A graph is said to be symmetric with respect to the x-axis if, for every point (x, y) on the graph, the point __________ is also on the graph. A graph is said to be symmetric with respect to the y-axis if, for every point (x, y) on the graph, the point ___________ is also on the graph. A graph is said to be symmetric with respect to the origin if, for every point (x, y) on the graph, the point ___________ is also on the graph.

Ex 1) Algebraically test for symmetry. x-axis?y-axis? origin?

CIRCLES!!! A CIRCLE is a set of points in the xy-plane that are a fixed distance from a fixed point. That fixed distance is the _________________ and that fixed point is called the ________________. The STANDARD FORM of an equation of a circle with radius r and center (h, k) is ________________________.

Ex 2) Write the STANDARD FORM of the equation of the circle with radius 5 and center (-3, 6).

Ex 3) Graph the equation:

More about CIRCLES!!! The GENERAL FORM of an equation of a circle is __________________________________________.

Ex 4) Graph the equation:

Ex 5) Find the GENERAL FORM of the equation of the circle whose center is (1, -2) and whose graph contains the point (4, -2).