Prove that the straight lines `x/a-y/b =m and x/a+y/b=1/m,` where `a and b` are `'m'` is a parameter, always meet on agiven positive real numbers and hyperbola.

Prove that the straight lines x/a-y/b =m and x/a+y/b=1/m, where a and b are given positive real numbers and 'm' is a parameter, always meet on a hyperbola.

Prove that the straight lines x/a-y/b =m and x/a+y/b=1/m, where a and b are given positive real numbers and 'm' is a parameter, always meet on a hyperbola.

The differential equation of the family of straight lines y = mx + a//m where m is the parameter, is

The differential equation of the family of straight line y=mx+(4)/(m) , where m is the parameter, is

The differential equation of the family of straight line y=mx+(4)/(m) , where m is the parameter, is

(i) Find the eccentricity of hyperbola whose latus rectum is half of its transverse axis. (ii) Prove that the straight lines (x)/(a)-(y)/(b)=mand(x)/(a)-(y)/(b)=(1)/(m) always meet at a hyperbola, where 'm' is a constant.

The locus of the point of intersection of lines (x)/(a)+(y)/(b)=lambda and (x)/(a)-(y)/(b)=(1)/(lambda), where lambda is a parameter, is

A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 and meets the coordinate axes at A and Bdot Show that the locus of the midpoint of A B is the curve 2x y(a+b)=a b(x+y)