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The equation of family of curves for which the length of normal is equal to the radius vector
Dear pallvi
let a general point on the curve (x,y)
length of radius vector = √x2 +y2
lengt of normal is =y√(1+(dy/dx)2)
given √x2 +y2 =y√(1+(dy/dx)2)
or x2 +y2 =y2(1+(dy/dx)2)
or x2 =y2(dy/dx)2
or dy/dx = ±x/y
ydy =±xdx
y2/2 =± x2/2 +c
y2 ± x2 =c
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