1
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Question

# If a curve passes through the point (2,72) and has slope (1âˆ’1x2) at any point (x,y) on it, then the ordinate of the point on the curve whose abscissa is âˆ’2 is:

A
32
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B
32
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C
52
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D
52
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Solution

## The correct option is A −32Let y=f(x) be the curve.Now, the slope of the curve at (x,y) is dydxAccording to the problem,dydx=1−1x2Integrating we get,y=x+1x+c [where 'x' is integrating constant]Gives the curve passes the (2,72)72=2+12+cor 72−52=cor, c=1So, the curve is y=(x=1x+1)For x=−2; y=−2−12+1=−1−12=−(32)Required coordinate is (−32).

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