The slope of the tangent at `(x , y)` to a curve passing through a point `(2,1)` is `(x^2+y^2)/(2x y)` , then the equation of the curve is

Explanation

`(dy/dx) = [(x^2 + y^2)/(2xy)]`

` ∴ (dy/dx) = (x/2y) + (y/2x) ......(1)`


Let `(y/x) = v`

`∴ x(dy/dx) – y = x^2(dv/dx)`

` ∴ (1/x)[x^2(dv/dx) + y] = (1/2v) + (v/2) ------ from (1)`

` ∴ x(dv/dx) + v = (v/2) + (1/2v)`

` ∴ x ∙ (dv/dx) = [(1 – v2)/(2v)] `
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