NIMCET 2012 Question Paper with solutions

${\mathit{x}}^2+{\mathit{y}}^2$ - 2xy - 4 (x + y - 1) = 0
⇒ ${\left(\mathit{x}-\mathit{y}\right)}^2$ = 4 {(x + y) - 1}
Here , x - y = 0 ... (i)
and x + y = 1 ... (ii)

On solving, we get
x = y = $\frac{1}{2}$
∴ Centre of parabola = $\left(\frac{1}{2},\frac{1}{2}\right)$
Then, its focus S' = $\left(12\times \frac{1}{2},2\times \frac{1}{2}\right)$
= (1 , 1)