Do Now Write the equation for the locus

Do Now Write the equation for the locus of points 5 units from the point (-5, 6)

The Circle Aim: What are the standard and general forms of the equation of a circle?

The Circle: Applications WHEELS

AND TABLE TOPS

Definition P(x, y) The circle is the locus (set) Radius of all points Center that are (h, k) equidistant from a given point called the center.

Definition The standard form of the equation of a circle with radius r and center at (h, k) is:

Solution to Do Now h=-5 k=6 (-5, 6)

Try This Graph the circle with center at (-2, -1) and radius 2 using a graphing calculator. . .

Steps: 1. Write equation in standard form. 2. Solve for y 3. Enter in calculator: y 1 & y 2 4. Set window

Solution Window x [-6. 4 , 3] By y [-4 , 2] . . .

Definition The general form of the equation of a circle is: Where a, b, and c are constant

Try This Write the equation of the circle with center at (-5, 6) and radius of 5 in general form

The equation of a circle is: Write the equation in standard form. Find the radius and coordinates of the center. Hint: Change to standard form by completing the square

Try This The equation of a circle is: Find the radius and coordinates of the center. Radius=0. 5 ; Center: (3, -2)

Also Try This is a circle with radius 7. Find the value of k. k=– 8

A(– 1, 6) and B(3, – 2) are endpoints of a diameter of a circle a)Write an equation of this circle b) What are the coordinates of the y-intercepts of this circle?

Solution y = – 2. 359 y = 6. 359