If the line joining the points `(0,3)a n d(5,-2)`is a tangent to the curve `y=C/(x+1)`, then the value of `c`is1 (b) `-2`(c) 4(d) none of theseA. 1B. -2C. 4D. none of these

If the line joining the points `(0,3)a n d(5,-2)`is a tangent to the c

1.	If the line joining the points `(0,3)a n d(5,-2)`is a tangent to the curve `y=C/(x+1)`, then the value of `c`is1 (b) `-2`(c) 4(d) none of theseA. 1B. -2C. 4D. none of these
Answer» Correct Answer - C The equation of the line joining (0,3) and (5,-2) is ` x+y-3=0 " "…(i) ` Suppose this line touches the curve `y=(C )/(x+1) " at " (alpha, beta ).` Then, ` ((dy)/(dx))_((alpha"," beta)) =` Slope of the line (i) ` rArr -(C)/((alpha+1)^(2))=-1 " "[ because (dy)/(dx)=- (C)/((x+1)^(2))]` ` rArr C=(alpha+1)^(2) " "...(ii) ` Also, ` (alpha,beta)` lies on the line (i) and the given curve. Therefore, ` alpha+ beta -3=0 " "...(iii) ` and, ` beta=(C)/(alpha+1) " "...(iv) ` Form (ii) and (iv), we get ` beta=alpha+1 " "...(v) ` Solving (iii) and (v), we get ` 2 alpha +1-3 =0 rArr alpha =1 ` Substituting ` alpha=1 ` in (ii), we get C = 4

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If the line joining the points `(0,3)a n d(5,-2)`is a tangent to the curve `y=C/(x+1)`, then the value of `c`is1 (b) `-2`(c) 4(d) none of theseA. 1B. -2C. 4D. none of these

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