HPC1.3 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?

2

2

4

1

xy

x

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: 2 23 2 16x y

More about CIRCLES!!!• The GENERAL FORM of an equation of a circle is__________________________________________.

Ex 4) Graph the equation: 2 2 4 6 12 0x y x y

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).