NIMCET 2016 Question Paper with solutions

Given locus is $\left(-1,1\right)$ and equation of directrix is $4\mathit{x}+3\mathit{y}-24=0$ The equation of axis which perpendicular to directrix is $3\mathit{x}-4\mathit{y}+\mathit{c}=0$
Point $\left(-1,1\right)$lies on above equation,$3\left(-1\right)-4\left(1\right)+\mathit{c}=0$
$\Rightarrow -3-4+\mathit{c}=0$
$\Rightarrow \mathit{c}-7=0$
$\Rightarrow \mathit{c}=7$
Then, equation of axis is$3\mathit{x}-4\mathit{y}+7=0$
Since. vertex lie on given axis
Therefore, only option (d) satisfy the above equation
Hence, vertex will be $\left(1,\frac{5}{2}\right)$