If the curve y=|x−3| touches the parabola y2=λ(x−4),λ>0, then length of latus rectum of the parabola(in units) is
A
2
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B
4
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C
16
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D
8
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Solution
The correct option is B4 The curve y=|x−3| can be rewritten as y={x−3,x≥33−x,x<3 Hence curve will touch the parabola y2=λ(x−4) for x≥3 as λ>0 Now, let X=x−4, then y2=λX and y=X+1
Now, using the tangency condition m=1,c=1⇒c=am⇒λ4=1⇒λ=4