Show that all curves for which the slope at any point `(x,y)` on it is `(x^2+y^2)/(2xy)` are rectangular hyperbola.

Show that the family of curves for which the slope of the tangent at any point (x,y) on it is (x^(2)+y^(2))/(2xy), is given by x^(2)-y^(2)=cx

Show that for rectangular hyperbola xy=c^(2)

Find the equation of a curve, passes through (-2,3) at which the slope of tangent at any point (x,y) is (2x)/(y^(2)) .

If a curve passes through the point (1, -2) and has slope of the tangent at any point (x,y) on it as (x^2-2y)/x , then the curve also passes through the point

The equation of the chord joining the points (x_(1) , y_(1)) and (x_(2), y_(2)) on the rectangular hyperbola xy = c^(2) is :

A family of curves is such that the slope of normal at any point (x, y) is 2(1-y). The orthogonal trajectories of the given family of curves is

A curve passes through the point "(2,0)" and the slope of tangent at any point (x,y) on the curve is x^(2)-2x for all values of x ,then the maximum value of y is equal to _____________