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Question

The equation of the curve whose tangent at any point (x, y) makes an angle tan1(2x+3y) with x-axis and which passes through (1, 2) is

A
6x+9y+2=26e3(x1)
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B
6x9y+2=26e3(x1)
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C
6x+9y2=26e3(x1)
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D
6x9y2=26e3(x1)
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Solution

The correct option is A 6x+9y+2=26e3(x1)
Given dydx=(2x+3y)
Let 2x+3y=z
2+3dydx=dzdx13(dzdx2)=dydx
13(dzdx2)=zdzdx=3z+2
dz3z+2=dxlog(3z+2)=3x+c
dz3z+2=dxlog(3z+2)=3x+c
3z+2=e3x+c
6x+9y+2=e3x+c...(1)
6+18+2=e3x+c
26=e3+cec=26.e3
Then the equation is 6x+9y+2=26e3(x1)

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