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1)

 The slope of the line touching both the parabola   y2=4x    and x2=32y is 


A) 12

B) 32

C) 18

D) 23

Answer:

Option A

Explanation:

 Let the tangent  to parabola be y=mx+a/m, If it touches the other  curve, then D=0, to get the value of m 

 For parabola, y2=4x 

  Let y=mx+1/m  be tangent line and it touches the parabola  x2=32y

      x2=32(mx+1m)

     x2+32mx+32m=0

     D=0

    (32m)24.(32m)=0

                        m3=18

                            m=12