1.5 Day 2 Circles
September 30, 2008
1.5 Circles
Objectives:
• Write the Standard Form of the equation of a circle.
• Write the General Form of the equation of a circle.
Given an equation
Given graph
graph.
equation.
Sep 18 ­ 2:22 PM
1
1.5 Day 2 Circles
September 30, 2008
A circle is a set of points in the xy plane that are a fixed distance r from a fixed point (h,k).
r
Derive the Standard Form of a circle by finding the distance between any point on the circle and the center.
radius = r
center = (h , k)
Sep 18 ­ 2:24 PM
2
1.5 Day 2 Circles
September 30, 2008
Write the Standard Form of the equation of a circle.
r2 = ( x ­ h )2 + ( y ­ k )2
1.
Write the equation of the circle with radius 1 and center at (0,0).
Sep 18 ­ 2:37 PM
3
1.5 Day 2 Circles
September 30, 2008
Write the Standard Form of the equation of a circle.
r2 = ( x ­ h )2 + ( y ­ k )2
Ex 1. Write the equation of the circle with radius 5 and center at (­3, 4).
Find the intercepts of the circle.
Graph the circle by hand.
Sep 18 ­ 2:37 PM
4
1.5 Day 2 Circles
September 30, 2008
Ex 2. Find the center, radius and intercepts of the circle:
r2 = ( x ­ h )2 + ( y ­ k )2
3(x + 1)2 + 3(y ­ 1)2 = 6
Sep 19 ­ 10:26 PM
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1.5 Day 2 Circles
September 30, 2008
Converting Standard Form
General Form
r2 = ( x ­ h )2 + ( y ­ k )2
x2 + y2 + ax + by + c = 0
Rewrite the circle in General Form:
(x + 3)2 + (y ­ 4)2 = 25
Sep 19 ­ 7:52 PM
6
1.5 Day 2 Circles
September 30, 2008
Sep 30­8:53 AM
7
1.5 Day 2 Circles
September 30, 2008
Converting General Form
Standard Form
r2 = ( x ­ h )2 + ( y ­ k )2
x2 + y2 + ax + by + c = 0
Write in standard form the equation given in General Form:
*Complete the square
x2 + y2 + 4x ­ 6y + 12 = 0
Sep 19 ­ 7:52 PM
8
1.5 Day 2 Circles
September 30, 2008
Finding the General Equation of a Circle
Find the general equation of the circle whose center is (1,­2) and whose graph contains the point (4,2).
General Form
x2 + y2 + ax + by + c = 0
Sep 19 ­ 8:12 PM
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1.5 Day 2 Circles
September 30, 2008
Homework
1.5 p. 49 #1­8, 10­18 even, 19­22, 24­36 even, 37­40, 52
Go Impalas!!!
Sep 19 ­ 8:22 PM
10