1. Graphing and Writing Equations
Circles
Graphing and Writing Equations

2. What is a circle? A conic formed when…. A second degree equation…
A locus of points…

3. Definition as a conic
A circle is a conic or a conic section because it is formed by the intersection of a plane and a double-napped cone.

4. Algebraic Definition A circle is defined as the second degree equation
Ax2+Bxy+Cy2 +Dx+Ey+F = 0
when A = C.

5. A circle is a locus of points…..
But, what is a locus…?
A locus is the set of all points, and only those points, that satisfy one or more conditions.
So, “ A locus of points in a plane 10 cm from a point A” gives a geometric description of a circle with center A and a radius of 10

6. Geometric Definition
A circle is the locus or collection of all points (x, y) that are equidistant from a fixed point, (h, k) called the center of the circle.
The distance r , between the center and any point on the circle is the radius

7. Using the distance formula, you can derive
the standard form of a circle.
(x- h)2 + (y- k)2 = r 2
where, center = (h, k) and radius = r

8. Equation of a circle:
Practice Problems to write the equation of a circle when given the center and the radius.

9. What if the center and radius are not given?
Try these :
Center = (0,3) and solution point = (0, 6)
Endpoints of diameter are (-2,3) and (6,5)
Center on the line y = 2, and tangent to the x-axis at (3,0)

10. Graph the circle
To graph a circle, locate all the points that are a fixed distance r, from the center (h, k).
Click here to graph a circle

11. Graph a circle with center at the origin
Example: Graph x2 + y2 = 4

12. To Graph a Circle center (h,k) and radius r
Example: (x-3)2+   (y-3)2 =4
Click Here To graph a circle if given a radius and a center

13. What are some applications?
Circular orbits of the earth for satellites.
Perfect shape for cross-section of a submarine.
Gears
Other