The Circle

I.  Homework

II.  Conic Sections

We will see that the conic sections can be formed by intersecting a plane with a cone.  A demo will be done in class.

III.  Circles

A circle is the set of points in a plane a fixed distance from a point.  By the Pythagorean Theorem, we have that the distance r from the center (h,k) of the circle to a point (x,y) on the circle is

r = sqrt[(x - h)2 + (y - k)2]

or

(x - h)2 + (y - k)2 = r2

Example:  Find the equation of the circle with center (2,1) and  radius 4.

Solution:   

We have:  (x - 2)2 + (y - 1)2 = 42 = 16

Exercise:

A)  Find the equation of the circle with center (1,3) and passing through the point (7,11)

Graph the following:

A)  (x - 2)2 + (y + 1)2 = 9

B)  x2 - 2x + y2 + 6y = 14

C)  x2 + y2 + 4x - 4y = 9

D)  x2 + y2 + 6x + 2y = 29

E)  Find the area between the circles:

x2 + y2 - 6x + 4y = 12

and

x2 + y2 - 6x + 4y = 23