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  • How to solve this problem- - Equation of a common tangent to the parabola and the hyperbola is : - Co-ordinate geometry - JEE Main

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

  • Option 1)

     

    4x+2y+1=0

  • Option 2)

     

    x-2y+4=0

  • Option 3)

    x+y+1=0

  • Option 4)

     

    x+2y+4=0

Answers (1)

best_answer

 

Equation of tangent -

y= mx+\frac{a}{m}

- wherein

Tengent to y^{2}=4ax is slope form.

 

As we know,

y=mx+\frac{1}{m} is equation of tangent to paralala y^{2}=4x

Since it is tangent to xy =2

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

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

D=0\Rightarrow 1+8m^{3}=0, m=\frac{-1}{2}

y=-\frac{x}{2}-2 \Rightarrow x+2y+y=0


Option 1)

 

4x+2y+1=0

Option 2)

 

x-2y+4=0

Option 3)

x+y+1=0

Option 4)

 

x+2y+4=0
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