Circles Lesson 13.6

Describe what each of the following equations make: 1.y = 4 2.3x + 2y = x 2 – 6x + 12 = 0 4.x 2 + y 2 = 9 1.Horizontal line. 2.Diagonal line. 3.Parabola 4.Circle

Introduction: The equation of a circle is based on the distance formula and the fact that all points on a circle are equidistant from the circle’s center.

Theorem 127 Circle equation: (x-h) 2 + (y-k) 2 = r 2 Where (h, k) is the center of the circle and r = radius

Write the equation for a circle whose center is (1,5) and has a radius of 4. (x-1) 2 + (y-5) 2 = 16 Find the center and radius of the graph (x+2) 2 + (y-1) 2 = 25 Center (-2,1) Radius = 5

Is x 2 – 8x + y 2 -10y = 8 an equation of a circle? ****Use the steps of completing the square to find out.**** x 2 – 8x + ____+ y 2 – 10y + ____= 8 Add ½b 2 to x, ½b 2 to y and both answers to the other side of the equal sign. Next, complete the square for the x & the y Center is (4,5) radius = 7 (x - 4) 2 + (y - 5) 2 = = 49

Write an equation of a circle with center (-5,0) and a radius of 3 / 2. (x-(-5)) 2 + (y-0) 2 = ( 3 / 2 ) 2 (x + 5) 2 + (y) 2 = 9 / 4

Find the center, radius, diameter, circumference and area of: (x+5) 2 + (y-2) 2 = First, get rid of the 3 by multiplying everything by 3. Center Radius Diameter Circumference Area (-5,2) Л 81Л

Describe the graph of (x-2) 2 + (y+5) 2 = 0 The center is (2,-5), the radius is 0. It is a circle that has shrunk to a single point! It is called a point circle.

Describe the graph of x 2 + (y-4) 2 = -25 Center is (0,4) and the radius is the square root of -25. However, the square root of -25 is not a real number, so it can’t be drawn on a coordinate plane. Since the square root of -25 is an imaginary number the equation is said to represent an imaginary circle.