EQUATION OF A CIRCLE

(x-h)²+ (y-k)² =r²

where (h,k)= center

center= (5,3) r=4

(x-5)² +(y+3)² =16

square root of 16 =4

graph 4 up down left and right from center

Given c(6,0) diameter =8

(x-6)²+(y-0)² =y²

write eq of circle when given in standard form

x2 +y2 -10c +9=0

rewrite the eq with x and y on left and constants on right

x2-10x +y2=-9

now complete the square (take ½ and ² it)

x2 -10x +_?=

x2 -10x +25+y2=-9+25

(x-5)2 +y2=16

so then what is the center and radius? (5,0) radius is 4

the center will have flipped signs

ex :(steps in brackets)

Q:x² +y² +6x -8y-11=0

(move constants to one side and put variables together)

x² +6x + y² -8y =11

(take half of the variable’s number and then square it ) (add the same to the other side)

x² 6x+9 +y²-8+16 = 11 +9+16

(add these)

(take the number used before and then square it with the x²)

(x+3)² +(y-4)²= 36

(root the final number to find radius)

( x+3)² + (y-4)² =6

radius =6

(flip the signs of the numbers in parentheses to find the center)

x=-3 y= 4 center=(-3,4)