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  • If the Reflection of the parabola y^2=4(x-1) in the line x+y=2 is the curve Ax+By=x^2, then the value of A+B is

If the Reflection of the parabola y^2=4(x-1) in the line x+y=2 is the curve Ax+By=x^2, then the value of A+B is

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Solution: We have ,

y^2=4(x-1)

General point P(t^2+1,2t)

Image of P w.r.t Linex+y-2=0

\ x-(t^2+1)/1=y-2t/1=-2(t^1+1+2t-2)/1+1\ \Rightarrow x-(t^2+1)/1=-(t^2+2t-1)/1\ \Rightarrow x=-2t+2 .....(1)\ \Rightarrow y-2t/1=-(t^2+2t-1)/1\ \Rightarrow y=(1-t^2).......(2)

From (1);and;(2) we get

y=1-[(x-2)^2/4]\ \ Rightarrow x^2=4x-4y\ \Rightarrow Hence;A+B=0

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Deependra Verma

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