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Question

If a variable tangent to the curve x2y=c3 makes intercepts a,b on x and yaxis respectively, then the value of a2b is

A
27c3
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B
427c3
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C
274c3
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D
49c3
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Solution

The correct option is C 274c3
x2y=c3
x2dydx+2xy=0
dydx=2yx
Equation of tangent at (x,y)
Yy=2yx(Xx)
Y=0, gives, X=3x2=a
and X=0, gives, Y=3y=b
Now,
a2b=9x24×3y
=274x2y=274c3

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