All about circle

r (x, y) A circle is a set of points in the xy-plane that are a fixed distance r from a fixed point (h,k). The fixed distance is called the radius, and the fixed point (h,k) is called the center of the circle. x y (x, y) r Center:(h, k)

The standard form of an equation of a circle with radius r and center (h,k) is

( ) x y + − = 1 3 16 2 Graph ⧭ x y ⧭ ⧳ ⧭ ⧭

Find the Equation of the Circle (-1,3) (3,3) (-1, 7) (-5, 3) (-1, -1) x y (x+1)2+(y-3)2=16

The general form of the equation of a circle

Find the center and the radius of First group terms:

Add appropriate terms to complete the squares for x and for y.

(x+5)2 + y 2 = 17 Distance Formula: Writing the equation of a circle given its center and a point on the circle The point(-6,4)lies on a circle whose center is at (-5,0)               . Find the equation of this circle. Distance Formula: The distance between the points P and Q is (x+5)2 + y 2 = 17

Writing the equation of a circle given the endpoints of a diameter Find the equation of the circle whose diameter has endpoints (2,3) and (-2,-5)               . x2 + (y-1) 2 = 29

Classwork 1. (0,0), 10 2. (-4,-6), 7 3. (2,3), 4.5 4. (-6,10), 1 Write the Equation of the circle with the given center and radius: 1. (0,0), 10 2. (-4,-6), 7 3. (2,3), 4.5 4. (-6,10), 1 Graph and find the center and radius of the following circle 1. x2 + y2 =4 2. x2 + (y+1)2 =9 3. (x+5)2 + y2 =81 4. (x+2)2 + (y+4)2 =25