The foot of the perpendicular from the origin to a plane is $(12,-4,3).$  Find the equation of the plane.  Enter your answer in the form
\[Ax + By + Cz + D = 0,\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\gcd(|A|,|B|,|C|,|D|) = 1.$
<|im_start|>system
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<|im_start|>user
The foot of the perpendicular from the origin to a plane is $(12,-4,3).$  Find the equation of the plane.  Enter your answer in the form
\[Ax + By + Cz + D = 0,\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\gcd(|A|,|B|,|C|,|D|) = 1.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12x - 4y + 3z - 169 = 0
The foot of the perpendicular from the origin to a plane is $(12,-4,3).$  Find the equation of the plane.  Enter your answer in the form
\[Ax + By + Cz + D = 0,\]where $A,$ $B,$ $C,$ $D$ are integers such that $A > 0$ and $\gcd(|A|,|B|,|C|,|D|) = 1.$
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