Circles
Graphing and Writing
Equations
What is a circle?
A conic formed when….
A second degree equation…
A locus of points…
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.
Algebraic Definition
A circle is defined as the second
degree equation
Ax2+Bxy+Cy2 +Dx+Ey+F = 0
when A = C.
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
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
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
Equation of a circle:
Practice Problems to write the equation of a
circle when given the center and the radius.
What if the center and radius are
not given?
Try these :
1. Center = (0,3) and solution point = (0, 6)
2. Endpoints of diameter are (-2,3) and (6,5)
3. Center on the line y = 2, and tangent to the x-axis at
(3,0)
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
Graph a circle with center at
the origin
Example: Graph x2 + y2 = 4
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
What are some applications?
1. Circular orbits of the earth for
satellites.
2. Perfect shape for cross-section
of a submarine.
3. Gears
4. Other