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in Differential equations by (36.3k points)

Find the curve such that the square of the intercept cut by any tangent off the y-axis is equal to the product of the co-ordinates of the point of tangency.

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Best answer

The equation of tangent to the curve at (x, y) is

Y – y = (dy/dx)(X – x)

Putting X = 0, we get

Y = y – x(dy/dx)

It is given that,

Integrating, 

we get 

2√v + log |x| = c

2√(y/x) + log |x| = c

which is the required solution.

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