Step-by-step explanation:
Hey there!
Given;
[tex] {x}^{2} + {y}^{2} - 4x + 12y = \: - 4[/tex]
Now, Try to make it a perfect square.
[tex] {x}^{2} - 4x + {(2)}^{2} - ( { 2)}^{2} + {y}^{2} + 12y + ( {6)}^{2} - ( {6)}^{2} = - 4 [/tex]
Make perfect square and shift -(2)^2 and -(6)^2 on right side.
[tex]( {x - 2)}^{2} ( {y + 6)}^{2} = - 4 + 40[/tex]
[tex]( {x - 2)}^{2} ( {y + 6)}^{2} = 36[/tex]
Comparing the equation with (x-h)^2(y-h)^2= r^2.
We get,
Centre (h,k)= (2,-6)
Radius (r) = 6
Hope it helps...
