Suppose two tangents drawn to a parabola at points A and B on it are  $\text{x+y+2=0\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}x-y+4=0\hspace{0.17em}}$. While the normals drawn at A and B meet at C (1,2) lying on its axis, then :

Tangents are perpendicular $\Rightarrow AB$  is focal chord and Normal meet on axis of parabola
$\Rightarrow$  AB is double ordinate  $\Rightarrow$ AB is latus rectum.
$\Rightarrow Z(-3,1)$ 
  Equation of axis
$\text{y-1=}\frac{\text{1}}{\text{4}}\left(\text{x+3}\right)$
$$\begin{gathered} \text{4y-4=x+3 } \\ \text{x-4y+7=0 } \\ \text{CZ=4a=}\sqrt{4^2+1^2}=\sqrt{17} \end{gathered}$$

Hence, A, B and C are the correct answers.