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Question

Tangent to a curve intercepts the y-axis at a point P. A line perpendicular to this tangent through P passes through another point (1,0) the differential equation of the curve is


A

ydydxx(dydx)2=1

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B

yd2ydx2+(dydx)2=0

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C

ydxdy+x=1

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D

None of these

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Solution

The correct option is A

ydydxx(dydx)2=1




The equation of the tangent at the point
R(h,f(h)) is yf(h)=f(h)(xh)
The coordinates of the point P are (0,f(h)hf(h))
The slope of the perpendicular line is f(h)+hf(h)
Applying the condition for perpendicularity
f(h)f(h)h(f(h))2=1ydydxx(dydx)2=1
which is the required differential equation to the curve y=f(x)


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