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1)

The normal at the point ( at21,2at1) on the parabola, cuts the parabola again at the point whose parameter is 


A) t2=t12t1

B) t2=t1+2t1

C) t2=(t1+2t1)

D) none of these

Answer:

Option C

Explanation:

 Let the normal at 't1'  cuts the parabola again at the point 't2' , the equation of the normal at  ( at21,2at1)  is y+t1 x =2at1 +at13

Since it passes through the point 't2' i.e,

 ( at22,2at1

       2at2+at1t22=2at1+at31

 2a(t1t2)+at1(t21t22)=0

2+t1(t1+t2)=0(t1t20)

2+t21+t1t2=0

 t1t2=(t21+2)t2=(t1+2t1)