Question

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

Answer 1

Answer:

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Answer 2

Answer:

We have, y

2

=2kx+k

2

(1)

Differentiating w.r.t. x, we get

yy

′

=k(2)

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

y

2

=2xyy

′

+(yy

′

)

2

For orthogonal trajectory, substituting y

′

with −

y

′

1

in (2), we get

y

2

=2xy(−

y

′

1

)+(

y

′

y

)

2

⟹(yy

′

)

2

=−2xyy

′

+y

2