A curve that passes through (2, 4) and having subnormal of constant length of 8 units can be;

y² = -16x + 24

Let the curve be y = f(x). Subnormal at any point = $\left|y \frac{d y}{d x}\right|$

$\Rightarrow y \frac{d y}{d x}= \pm 8 \Rightarrow y dy= \pm 8 dx \Rightarrow \frac{y^2}{2}= \pm 8 x+c$

$\Rightarrow y^2=16 x+2 c_1, \Rightarrow c_1=-8$  or  $y^2=-16 x+2 c_2, \Rightarrow c_2=24$

Hence (2) are correct answer.