#5 Conics ­ Completing the Square Circle Equations.notebook
Warm Up 4/10/15
April 10, 2015
4/10 - Writing Equations of Circles using Completing the Square
Objective: To use completing the square in equations of circles
Identify the center and radius of each. 1.
2.
3.
4.
REVIEW OF CIRCLE EQUATIONS:
Referred to as "center‐radius form" OR "standard form"
(x ‐ h)2 + (y ‐ k)2 = r2
center (h,k)
radius
BUT circles are often given in "general form":
ax2 + by2 + cx + dy + e = 0
May 9­2:48 PM
Steps to Write the Equation of a Circle in Standard Form
Write the standard form equation of the circle.
x2 + y2 ­ 4x ­ 6y + 8 = 0
May 9­2:53 PM
Examples
Write each equation in standard form and find the center and
radius of the circle.
1. x2 + y2 ­ 4x + 10y + 20 = 0
1. Move the constant to the right side of the equation and group your x's together and your y's together.
2. Complete the square for both the x's and the y's.
2. 2x2 + 2y2 + 6x ­ 8y + 12 = 0
3. Turn each perfect square trinomial into a binomial squared.
May 10­6:45 AM
You Try!
Write each equation in standard form and find the center and
radius of the circle.
1. x2 + y2 ­ 12x + 8y + 16 = 0
May 10­6:56 AM
CLOSURE
At the top of your homework, explain the steps to write the equation of a circle in standard form when given an equation in general form.
2. 3x2 + 3y2 ­ 54x + 51 = 0
HOMEWORK
"Completing the Square Day 2 & 3" Worksheet
Page 3 and 4
Apr 8­9:00 PM
May 9­3:09 PM
#5 Conics ­ Completing the Square Circle Equations.notebook
Apr 10­9:49 AM
April 10, 2015