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Math

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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?

  • 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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