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If a curve passes through the point (1, ...

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as `(x^2-2y)/x`, then the curve also passes through the point

A

(-1, 2)

B

`(sqrt(3), 0)`

C

(3, 0)

D

`(-sqrt(2), 1)`

Text Solution

Verified by Experts

The correct Answer is:
B
given `(dy)/(dx) = (x^(2) - 2y)/(x) , (dy)/(dx) + (2)/(x)y = x`
I.F = `e^(int(2)/(3)dx) = e^(2nx) = x^(2)`
Multiplying both sides by `x^(2) , (d)/(dx) (y.x^(2)) = x^(3)`
Integrating both sides , `y.x^(2) = (x^(4))/(4)+c`, It passes through (1, -2)
`c = (-9)/(4), y = (x^(2))/(4) -(9x^(-2))/(4) = (x^(2) - 9x^(-2))/(4)`
It passes through `(sqrt(3), 0)`
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