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Given that the slope of the tangent to a...

Given that the slope of the tangent to a curve ` y = f(x) ` at any point ` (x, y )` is `(2y )/ ( x ^ 2 )`. If the curve passes through the centre of the circle ` x ^ 2 + y ^ 2 - 2 x - 2y = 0 ` , then its equation is :

A

` x log _ e |y| = 2 ( x - 1 ) `

B

` x ^ 2 log _e |y| = - 2 ( x - 1 ) `

C

` x log _ e |y| = x - 1 `

D

`x log _ e |y| = - 2 ( x - 1 ) `

Text Solution

Verified by Experts

` ( dy ) /(dx ) = ( 2y ) /(x ^ 2 ) rArr ln y = - ( 2 ) /( x ) + ln C `
passes through ` (1, 1 ) `
` 0 = ( -2 ) /(1) + ln C, ln C = 2 `
`ln |y| = - ( 2 ) /( x ) + 2 `
` x ln |y| = 2 ( x - 1 )`
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