The equation of a common tangent to the curves, y ^ 2 = 16x and xy...

A tangent to the parabola ${y}^{2} = 16x$ can be written as:
$y = mx + \dfrac{4}{m}$ …. (1)
It will touch the hyperbola $xy = – 4,$ if the quadratic $x\left(mx + \dfrac{4}{m}\right) = – 4$ has coincident roots,
$⇒ \left({m}^{2}\right){x}^{2} + 4x + 4m = 0, D ≡ 16 - 16{m}^{3} = 0$
$⇒ m = 1$
$⇒$ Equating of common tangent will be $y = x + 4$
$⇒ x - y + 4 = 0$