Question

What is the focus of the parabola given by the equation x = 3(y – 1)2 + 2?

Answer 1

\[3\left( y-1 \right)^{2}=x-2\]
\[\left( y-1 \right)^{2}=\frac{ 1 }{ 3 }\left( x-2 \right)\]
vertex is (2,1)
4a=3
\[a=\frac{ 1 }{12 }\]
\[focus is ( 2+\frac{ 1 }{12 } ,1) i.e.,(\frac{ 25 }{12 },1)\]