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

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

1. A

$4x+2y+1=0$

2. B

$x+2y+4=0$

3. C

$x+y+1=0$

4. D

$x-2y+4=0$

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### Solution:

Let the equation of tangent to parabola

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

It is also a tangent to hyperbola .

[From (i)]

Now, $D=0⇒1/{m}^{2}+8m=0⇒m=-1/2$

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

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