Circles (Graphing)

Equation Of A Circle, Graphing A Circle

What is the equation of a circle?

(x-a)²+(y-b)²=r²

What do the variables in the equation of a circle represent?
(x-a)²+(y-b)²=r²

The centre of the circle is (a,b). “a” being the x and “b” being the y value. The radius of the circle is “r”

How is the equation of a circle formed using the pythagoras theorem?

(x)²+(y)²=r²
a and b aren’t here because we are assuming they are 0 (the circle is centered direcly on the origin).

Find the radius, centre point, x/y intercept for this equation of a circle
(x)²+(y-2)²=4

r²=4 so r=√4=2. Radius=2

Centre point=(a,b)=(0,2) 

x int= (x)²+(0-2)²=4   =x²+(-2)²=4   =x²+4=4   x²=0 x=0    x intercept is (0,0)

y int= (0)²+(y-2)²=4   (y-2)²=4   y-2=±2 (there are 2 y ints because √4= -2 or +2)  

y int (1)= 4      (0,4)

y int (2)= 0      (0,0)

For the equation (x-4)²+(y-1)²=9
Find the x intercepts, y intercepts (to 2 d.p) and the centre of the graph

x ints= (x-4)²+(0-1)²=9   (x-4)²+(-1)²=9   (x-4)²+1=9   (x-4)²=8   

x-4= ±√8   x=±√8+4   1) (6.83,0)   2) (1.17,0)

y ints= (0-4)²+(y-1)²=9   (-4)²+(y-1)²=9   16+(y-1)²=9
(y-1)²=-7   y-1=√-7   The square root of a negative number is impossible since there is no same number multiplied by itself to create a negeative number. 
In conclusion there is no y-intercept

The centre of the graph is shown in the equation (x-4)² means the x of the centre is positive 4 and (y-1)² is postive 1 

Centre of graph= (4,1)

Graph the equation (x+5)²+(y+2)²=4

Since the 2 numbers are postive in the equation the centre are both in the negatives. (Opposites)