Question

find the differential equitation of the curve : y3=2kx+k2​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

sorry I don't have answer of

this answer but I know

the answer of this

type of question.

We have, y2=2kx+k2(1)

Differentiating w.r.t. x, we get

yy′=k(2)

Eliminating k, from (2) using (1), we get

y2=2xyy′+(yy′)2

For orthogonal trajectory, substituting y′with −y′1 in (2), we get

y2=2xy(−y′1)+(y′y)2

⟹(yy′)2=−2xyy′+y2

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I hope it will help.