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October 21, 2013

October 21, 2013
Today's Agenda: 1) HW Collection & Warm-up 2) Circles, from the ground up 3) Examples 4) Funner Examples -- I LOVE GEOMETRY!! Today's Learning Goals: Use the definition of a circle to derive its equation Solve problems algebraically involving circles Tonight's HW: Problem Set W [Due Wednesday] Begin Graded Problem Set Announcements: HW Quiz on Thursday (Problem Sets I & W) Graded Problem Set due Tuesday, November 15 Office Hours: Wednesday 8:05 - 8:32; Thursday 7:20 - 8 am

HW Collection
Please collect all of your work from the last unit -- Problem Sets A, B, Y, and the Test Review -- staple them together, make sure your name is on the packet, and turn them in.

Warm-up
1. Find the distance between (-1, 5) and (4, 3).

2. What is the midpoint of (4, 1) and (2, 8)?

October 21, 2013

Circles
What is a circle?
A circle is the set of all points in a plane that are equidistant from a fixed point, called the center. The fixed distance from the circle's center to any point on the circle is called the radius.

Suppose (h, k) is the center of a circle with radius r. Suppose (x, y) is any point on this circle. Write an equation for (x, y) based on the definition of a circle.

This leads us to the Standard Form of the Equation of a Circle:

(x - h)2 + (y - k)2 = r2
where (h, k) is the center of the circle and r is the radius.

Examples
A circle has center (2, -7) and radius 5.

1) Find the Standard Form of the equation of this circle.

2) Find the four easy points of the circle. Use them to sketch its graph.

3) Find another point on the circle.

4) Find the domain and range of this relation.

October 21, 2013
General Form of the Equation of a Circle
The General Form of the Equation of a Circle:

x2 + y2 + Dx + Ey + F = 0
1) Rewrite (x - 3)2 + (y + 4)2 = 10 in general form.

2) Rewrite x2 + y2 + 10x - 2y + 4 = 0 in standard form. Identify the center and radius of this circle.

Equation Templates for Various Functions
Circle:

Line:

Parabola/Quadratic:


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