Writing the Equation of a Circle We will be using the completing the square method for this, so lets remember…
Completing the Square Perfect Square Trinomials: Factor: This is called a perfect square trinomial because the factors are the same. So we can rewrite these factors as: This fact is going to help us during the process of completing the square!
Completing the square method: Steps: 1.Get all variables grouped together on one side of the equation, and all the constants on the other side of the equation (if coefficient of the squared term is not one, you must divide everything by it) 2.Take half of the coefficient of the non- squared variable term, square it, and add it to both sides 3.Factor the perfect square trinomial and write it as a binomial squared 4.Square root both sides to get rid of square from the binomial (don’t forget, when introducing a square root into the problem, your constant will have a +/- in front of it 5.Solve the two equations for the variable to get your roots #8: 4 4 Roots:
Page 3 Group by variable Get Constant on other side
Page 3 Group by variable Get Constant on other side
Page 3 Group by variable Get Constant on other side
Page 3 Group by variable Get Constant on other side
Writing the equation of a circle given the center and a point on the circle: Page 4 Steps: 1.Graph the points 2.Draw a triangle 3.Find length of radius using Pythagorean 4.Write equation of circle using center and radius.
Page 4
Homework Page 3 #2,6,8,10 Page 4 #3,5,6