Answer:
k=3
Step-by-step explanation:
Given equation is
[tex]x^2+y^2 -6y-12=0[/tex]
First we move -12 to the other side by adding 12 on both sides
[tex]x^2+y^2 -6y =12[/tex]
We apply completing the square method to get square form (y-k)^2
Lets take coefficient of y and then divide it by 2
-6 divide by 2 is -3
Then we square it (-3)^2 = 9
We add 9 on both sides
[tex]x^2+y^2 -6y + 9=12+9[/tex]
[tex]x^2+(y^2 -6y + 9)=21[/tex]
Now we factor, y^2 - 6y +9 is (y-3)(y-3)= (y-3)^2
[tex]x^2+(y-3)^3=21[/tex]
Now we compare with x^2 + (y-k)^2 = 21 and find the value of k
The value of k = 3
