Equation of a common tangent to the parabola y^2=4x and the hyperbola xy=2 is:

Question

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

Accepted Answer

Let the equation of tangent to parabola

y2 = 4x  be  y = mx + $${1 \over m}$$

It is also a tangent to hyperbola xy = 2

$$ \Rightarrow $$  x$$\left( {mx + {1 \over m}} \right)$$ = 2

$$ \Rightarrow $$  x2m + $${x \over m}$$ - 2 = 0

D = 0 $$ \Rightarrow $$   m = - $${1 \over 2}$$

So tangent is 2y + x + 4 = 0

Solutions · 1