Answer: The correct option is
(B) \((y-6)^2=9.\)
Step-by-step explanation: We are given to select the equation that is formed when completing the square on the following equation :
\(y^2-12y=-27~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We will be using the following formula :
\(a^2-2ab+b^2=(a-b)^2.\)
From equation (i), we have
\(y^2-12y=-27\\\\\Rightarrow y^2-2\times x\times6=-27\\\\\Rightarrow y^2-2\times x\times 6+6^2=-27+6^2\\\\\Rightarrow (y-6)^2=-27+36\\\\\Rightarrow (y-6)^2=9.\)
Thus, the required equation that is formed is \((y-6)^2=9.\)
Option (B) is CORRECT.
