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The curve y-e^(xy)+x=0 has a vertical ta...

The curve `y-e^(xy)+x=0` has a vertical tangent at the point:

A

(1, 1)

B

at no point

C

(0, 1)

D

(1, 0)

Text Solution

Verified by Experts

The correct Answer is:
D
The equation of the curve is
`y-e^(xy)+x=0`
`rArr (dy)/(dx)-e^(xy)(y+x(dy)/(dx))+1=0`
`rArr (dy)/(dx)(1-e^(xy))=ye^(xy)-1 rArr (dx)/(dy)=(1-xe^(xy))/(ye^(xy)-1)`
Clearly, `(dx)/(dy) =0` at (1, 0). So, required point is (1, 0).
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OBJECTIVE RD SHARMA ENGLISH-TANGENTS AND NORMALS-Chapter Test
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  11. The curve y-e^(xy)+x=0 has a vertical tangent at the point:

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  13. The length of the normal at t on the curve x=a(t+sint), y=a(1-cos t), ...

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  19. If m be the slope of the tangent to the curve e^(2y) = 1+4x^(2), then

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  20. If the curve y=ax^(3) +bx^(2) +c x is inclined at 45^(@) to x-axis at...

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  21. If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the lin...

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