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Find value of c such that line joining t...

Find value of c such that line joining the points (0, 3) and (5, -2) becomes tangent to curve `y=c/(x+1)`

Text Solution

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`xy + y = c`
`xy' + y + y' = 0`
`y' = -y/(1+x)`
`y|_(x_1, y_1) = -y_1/(1 +x_1)`
`(0,3) & (5,-2)`
`m = (3+2)/(0-5) = -1`
`+ y_1/(1 + x_1) = m = -1`
`x_1 + 1 = y_1`
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