# Math

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A circle has the equation
x^2+y^2+6x-46=0
A) how do i graph this properly
B) intercept are?

• Math -

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

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