A normal at any point (x, y) to the curve y = f(x) cuts the triangle of the unit area with the axes. The equation of the curve is?
1
\({y^2} - {x^2}{\left( {\frac{{dy}}{{dx}}} \right)^2} = 4\frac{{dy}}{{dx}}\)
2
\({x^2} + 2xy\frac{{dy}}{{dx}} + {y^2}{\left( {\frac{{dy}}{{dx}}} \right)^2} = 2\frac{{dy}}{{dx}}\)
3
\({x^2} - {y^2}{\left( {\frac{{dy}}{{dx}}} \right)^2} = \frac{{dy}}{{dx}}\)
4
\(x + y\frac{{dy}}{{dx}} = y\)