A circle has the equation
x^2+y^2+6x-46=0
graph using (h,k) radius r
A) how do i graph this properly
B) intercept are?
x ^ 2 + y ^ 2 + 6 x - 46 = 0
x ^ 2 + y ^ 2 + 6 x = 46
( x ^ 2 + 6 x + 9 ) + y ^ 2 = 46 + 9
( x + 3 ) ^ 2 + y ^ 2 = 55
The circle equation is:
(x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2
where a and b are the x and y coordinates of the center of the circle.
In this case :
a = - 3
becouse :
x + 3 = x - ( - 3 )
b = 0
Coordinates of the center of the circle :
( - 3 , 0 )
Radius r = sqrt ( 55 )
becouse :
sqrt ( 55 ) ^ 2 = 55
y intercept = points when x = 0
In this case :
( 0 + 3 ) ^ 2 + y ^ 2 = 55
9 + y ^ 2 = 55
y ^ 2 = 55 - 9 = 46
y ^ 2 = 465
y = + OR - sqrt ( 46 )
Coordinates of y intercepts :
0 , - sqrt ( 46 )
and
0 , - sqrt ( 46 )
x intercept = points when y = 0
In this case :
( x + 3 ) ^ 2 + 0 ^ 2 = 55
( x + 3 ) ^ 2 = 55
x + 3 = + OR - sqrt ( 55 )
x = + OR - sqrt ( 55 ) - 3
Coordinates of x intercepts :
- sqrt ( 55 ) - 3 , 0
and
sqrt ( 55 ) - 3 , 0