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Q.

If x + 4y = 14 is a normal to the curve y2αx3β at (2,3) then the value of α+β is___

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answer is 9.

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Detailed Solution

y2=αx3β or dydx=3αx22y
Therefore, slope of the normal at (2,3) is 
dxdy(2,3)=2×33α(2)2=12α=14
or α=2 
Also, (2,3) ;lies on the curve. Therefore,
9=8αβ or β=169=7 or α+β=9

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