deerhunter15
  • deerhunter15
The equation below represents a circle. x​2​ + ​y​2​ + 4​x​ – 2​y​ = ​a Part A: What is the ​x​ coordinate of the center of the circle? Part B: What is the ​y​ coordinate of the center of the circle? Part C: What is the value of ​a​ in the equation if the radius of the circle is 8?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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welshfella
  • welshfella
do you know how to complete the square?
deerhunter15
  • deerhunter15
no @welshfella I've never learned this stuff :/
deerhunter15
  • deerhunter15
@welshfella

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welshfella
  • welshfella
x^2 + 4x = (x + 2)^2 - 4 you divide the coefficient of x by 2 - in this case its 4/2 = 2 so this gives(x + 2) ^2 when you expand that you get +4 so you have to subtract 4 so that its = to x^2 + 4x.
welshfella
  • welshfella
we intend to convert the equation of the circle to the standard form (x - a)^2 + (y - b)^2 = r^2 here (a,b) is the center of circle and r = radius
welshfella
  • welshfella
so comparing (x - a) and ( x + 2) we see that -a = + 2 give a = -2 so -2 is the x coordinate of the center of circle
welshfella
  • welshfella
now you can work out the y coordinate in a sismilar way by completing the square on y^2 - 2y
welshfella
  • welshfella
try doing that
deerhunter15
  • deerhunter15
ok I will try
welshfella
  • welshfella
I'll start you off;- y^2 - 2y divide -2 by 2 = -1 so we have (x - 1)^2 - A what will A be?
deerhunter15
  • deerhunter15
-1x^2=A @welshfella
welshfella
  • welshfella
no A willo be -1 because (x - 1)^2 = x^2 - 2x + 1 so to get this back to x^2 - 2x we have to subtract 1
deerhunter15
  • deerhunter15
oh
deerhunter15
  • deerhunter15
@welshfella whats y?

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