A curve passing through the point (1,1) is such that the intercept made by a tangent to it on x-axis is three times the x co-ordinate of the point of tangency, then the equation of the curve is:
A
y=1x2
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B
y=√x
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C
y=1√x
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D
none
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Solution
The correct option is Cy=1√x Equation of tangent on any point on the curve is, Y−y=dydx(X−x) Thus intercept on the x-axis is,Ix=x−ydy/dx Now using given condition, Ix=x−ydy/dx=3x ∴ydxdy+2x=0 or dx2x+dyy=0 or 12logx+logy=k or logy√x=ek=constant Now given this curve passing through (1,1) ⇒k=0 ∴ Hence required curve is, y=1√x