Geometry Honors Section 9.6 Circles in the Coordinate Plane

If you graph the equation y = 3x + 5, its graph is a ____ so it is called a ______ equation. line linear

For the equation y = 3x + 5, 3 is the ______ of the line and 5 is the __________ of the line. Just by looking at the equation, you can determine the slope and y- intercept of the line without graphing. For this reason, the equation is said to be written in _____________ form. slope y-intercept slope-intercept

Similarly, there is a special form for the graph of a circle. This equation has the unofficial name of the form of a circle. center- radius

Recall that a circle is the set of points in a plane, that are equidistant from a given point.

Example 1: Use the distance formula to determine the three distances below. Show your initial use of the distance formula. CO = HO = KO =

In addition to equaling the same distance, what do the three distance formula have in common?

Using x and y as coordinates of any point on the circle, what would the distance formula look like for OO?

Squaring both sides we get the center-radius form of a circle. Center:_______ Radius: _______ (h, k) r

Example 1: Write an equation for the circle with the given center and radius. a) center: (4, 3)radius = 7 b) center (5, -2) radius =

Example 2: Find the center and radius of each circle. a) center ( ____, ____ ) r = _____ b) center ( ____, ____ ) r = _____

Example 3: Write the equation of the circle to the right.

Example 4: Write an equation of a circle with a center of (3, 4) containing the point (8, -8).

Example: The equation of a circle is x 2 + y 2 – 6x + 2y = b. Find the center of the circle. If the radius of the circle is 8 units, determine the value of b.

Fix problems 13 & 14 in the HW 13. x 2 + 8x + y 2 +12y = x x + y 2 +3y = 10