differential equation challenge 3 and 4 and 5 and 6!!!

5.find the curve for which the portion of tangent of the curve intercepted between the coordinate axis is of constant length.

6.find the family of curves which are such that the area of rectangle constructed on the absicca of any point and the initial ordinate of the tangent at that point is constant.
[also plz explain wht does initial ordinate of the tangent at that point mean...]

8 Answers

62
Lokesh Verma ·

5.find the curve for which the portion of curve intercepted between the coordinate axis is of constant length.

Do you mean the tangent or the normal..

because otherwise every curve is fixed and the distance intercepted between the coordintes is always constant!!!!

1
RAY ·

sorry dat was tangent..:)...n how will u be solvinmg the equationg u get wid dy/dx inside root.......

62
Lokesh Verma ·

take y=f(x)

take h, k on the curve such that f(h) = k

write the equation of the tangent.... y-k = dy/dx (at h,k) times (x-h)

find the x intercept and y intercept

the sum of thier squares is a constant

now solve it :)

19
Debotosh.. ·

yes...i was also going for that method!!! these kind of problems have appeared in JEE several times!

1
RAY ·

arre bhaiya wahi toh solve nahi ho raha...aap likh kar toh dekhiye........

n wht does the second sum mean????

1
Apprentice Of Devil ·

hot numerics guys...noone got brainz to solve em yet??

1
Philip Calvert ·

For 5 I think one such curve is

x2/3 + y2/3 = a2/3

1
RAY ·

yes true..but gimme the process yaarrr

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