13.6 Circles

T127 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

Complete the square! Is x 2 – 8x + y 2 -10y = 8an equation of a circle? x 2 – 8x + ____+ y 2 – 10y + ____= 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 (x-(-5)) 2 + (y-0) 2 = ( ) 2 (x+5) 2 + (y) 2 =

Find the center, radius, diameter, circumference and area of: (x+5) 2 + (y-2) 2 = 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.

Equation for a circle (x-h) 2 + (y-k) 2 = r 2 To find the length of the radius, take the square root of each side. Does this look familiar? Distance formula