1992...solve by shortest method.....plzzzzz

What normal to curve y=x2 forms shortest chord?????

5 Answers

62
Lokesh Verma ·

i think you know where the next point of normal at at^2,2at of a parabola meets

then the distance is given by ....

I guess this should be small only!

1
Samarth Kashyap ·

the normal at t meets the other point on the parabla at -t -2/t

calculating the distance and minimising i think u get the ans

1
Samarth Kashyap ·

ooops
i think the formula is for y2=4ax
plese verify

1
The Race begins... ·

yes, that formula is derived for y2=4ax curve. we can't generalize it !

for this parabola x2=y, let P(t1,t12) and let normal at P meet the parabola again at Q(t2,t22)

since normal is perpendicular to tangent (:P), (slope of normal)x(slope of tangent)=-1

=> (t2-t1)2t1 = -1 => t2= t1 - 1/2t1

i hope it's easy from here. :)

correct me if i am wrong !

24
eureka123 ·

ok............
my method was same as u all...........but i was looking for something even shorter than this...............

anyways thanx...

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