Prove that the straight lines `(x)/(a) - (y)/(b) = m and (x)/(a) + (y)/(b) = (1)/(m)` always meet on the hyperbola.

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.

If m is a variable,then prove that the locus of the point of intersection of the lines (x)/(3)-(y)/(2)=m and (x)/(3)+(y)/(2)=(1)/(m) is a hyperbola.

The locus of point of intersection of the lines (x)/(a)-(y)/(b)=m and (x)/(a)+(y)/(b)=(1)/(m)(i) a circle (ii) an ellipse (iii) a hyperbola (iv) a parabola

The locus of the point of intersection of the straight lines (x)/(a)+(y)/(b)=lambda and (x)/(a)-(y)/(b)=(1)/(lambda) ( lambda is a variable), 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 B. Show that the locus of the midpoint of AB is the curve 2xy(a+b)=ab(x+y)

Prove that the straight line x+y=1 touches the parabola y=x-x^(2)

Prove that the parallelogram formed by the straight lines : (x)/(a)+(y)/(b)=1 , (x)/(b)+(y)/(a)=1 , (x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 is a rhombus.

Prove that the straight lines x/alpha=y/beta=z/gamma,x/l=y/m=z/n and x/(a alpha)=y/(b beta)=z/(c gamma) will be co planar if l/alpha(b-c)+m/beta(c-a)+n/gamma(a-b)=0

The equation of the line passing through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1,(x)/(b)+(y)/(a)=1 and having slope zero is