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A tangent at a point P on the curve cuts...

A tangent at a point P on the curve cuts the x-axis at A and B is the foot of perpendicular from P on the x axis. If the midpoint of AB is fixed at `(alpha,0)` for any point P, find the differential equation and hence find the curve.

Text Solution

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here, ` y=f(x)`
`Y - y = dy/dx*(X-x)`
putting Y=0 `-y = dy/dx*(X-x)`
`X= x- y*dy/dx`
C is the mid point of AB
let coorinates of C as `(alpha,0)`
`C(alpha,0) = ((x+x - y*(dy/dx))/2 , 0)`
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