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  • Let the curve C be the mirror image of the parabola y^2=4x with respect to the line x+y+4=0. if A and B are the point of intersection of C with the line y=-5 ,then the distance between A and B is

Let the curve C be the mirror image of the parabola y^2=4x with respect to the line x+y+4=0. if A and B are the point of intersection of C with the line y=-5 ,then the distance between A and B is

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Solution:  We have ,

                 y^2=4x   and   x+y+4=0   

            Intersection point of line   x+y+4=0 and   y=-5.

       Rightarrow                                    x-5+4=0Rightarrow x=1

          Intersection point parabola y^2=4x and   Image line w.r to given line x+y+4=0

                          y^2=4xRightarrow y^2=4Rightarrow y=pm 2

        Hence ,                P(1,2)   and     Q(1,-2)

      herefore                                       PQ=AB=4.    

Posted by

Deependra Verma

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