The tangent at P(x, y) is
Y – y = (dy/dx)(X – x)
If p be the length of perpendicular from the origin, then
Hence, the result.
Also,
Integrating, we get
log |v2 + 1| + log |x| = log c
(v2 + 1)x = c
((y/x)2 + 1)x = c
x2 + y2 = cx
which is the required equation of the curve.