Question

Kength of the faugent ( =[y cdot sqrt{1+left(frac{d x}{d y}right)^{2}}] )
( f=y=y^{2}left[1+left(frac{d x}{d y}right)^{2}right] )
( = )
( Rightarrow quad frac{d y}{d x}=pm frac{y}{sqrt{1-y^{2}}} )
- ( int frac{sqrt{1-y^{2}}}{y} d y=pm x+c )
Det assuming ( y=sin theta, d y=cos theta d theta )
( 8 quad sqrt{1-y^{2}}+ln left|frac{1-sqrt{1-4^{2}}}{4}right|=pm x+c )

# If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve. [JEE 2005 (Mains)] [30118116171

Solution