The normal to the curve x=at2,y=2at at the point P(t) meets the curve again at Q(t′). Then t′ is
A
t+1t
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B
−t−2t
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C
t+2t
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D
t−1t
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Solution
The correct option is C−t−2t Normal at x=at2,y=2at is given by, y+tx=2at+at3 Given it also passes through Q(t′) which is x=at′2,y=2at′ ⇒2at′+at′2t=2at+at3 ⇒2(t′−t)=t(t2−t′2)=t(t+t′)(t−t′) ⇒2=−t(t+t′) (since t≠t′) ⇒t′=−2t−t