Find the locus of image of the veriable point `(lambda^(2), 2 lambda)` in the line mirror x-y+1=0, where `lambda` is a perimeter.
Text Solution
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Let the image of `(lambda^(2), 2 lambda)` in the line mirror x-y+1=0 be (h,k). `therefore (h-lambda^(2))/(1) = (k-2lambda)/(-1) = (-2(lambda^(2)-2lambda +1))/(2)` `therefore h+1 = 2lambda " " (1)` `" and " k= lambda^(2) + 1 " " (2)` Putting the value of `lambda` from (1) in (2), we get `k-1 = ((h+1)/(2))^(2)` or 4(y-1) = `(x+1)^(2)` This is the required locus.
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