Equation of a common tangent to the parabola y2=4x and the hyperbolaxy=2 is

Let the equation of tangent to parabola

$y^{2} = 4 x$ be $y = m x + 1 / m$ …(i)

It is also a tangent to hyperbola $x y = 2$ .

$\Rightarrow x (m x + \frac{1}{m}) = 2$ [From (i)]

$\Rightarrow x^{2} m + x / m - 2 = 0$

Now, $D = 0 \Rightarrow 1 / m^{2} + 8 m = 0 \Rightarrow m = - 1 / 2$

$∴$ Equation of tangent is $y = - \frac{1}{2} x - 2$

$\Rightarrow 2 y + x + 4 = 0$

Equation of a common tangent to the parabola $y^{2} = 4 x$ and the hyperbola $x y = 2$ is