Let a tangent to the curve y² = 24x meet the curve xy = 2 at the points A and B. Then the mid points of such line segments AB lie on a parabola with the

Let P(x₁, y₁) be midpoint of AB of curve xy = 2 then equation of AB is S₁ = S₁₁
$\Rightarrow \frac{1}{2}\left({\mathrm{xy}}_1+{\mathrm{x}}_1\mathrm{y}\right)=\frac{1}{2}{\mathrm{x}}_1{\mathrm{y}}_1$
$\Rightarrow$xy₁ + x₁y - x₁y₁ = 0 is tangent of y² = 24x
$\Rightarrow$am² = In
Locus is 6(x₁²) = y₁(-x₁y₁)
Locus is y² = -6x
Directrix is 4x = 3