Prove that the parallelogram formed by the 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 diagonals of the parallelogram formed by the four lines : x/a +y/b=1,x/b+y/a= 1, x/a + y/b = -1 and x/b + y/a = -1 are at right angles .

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals.

The point of intersection of the lines x/a+y/b=1 and x/b+y/a=1 lies on

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 angle between the st. lines : (a + b)x + (a-b)y = 2ab and (a-b)x+(a+ b) y = 2ab is tan^-1 frac(2ab)(a^2-b^2) .

The point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1 does not lie on the line

Area of the quadrilateral formed with the foci of the hyperbola x^2/a^2-y^2/b^2=1 and x^2/a^2-y^2/b^2=-1 (a) 4(a^2+b^2) (b) 2(a^2+b^2) (c) (a^2+b^2) (d) 1/2(a^2+b^2)

Find the area of the smaller region bounded by the ellipse x^2/a^2 + y^2/b^2 = 1 and the straight line x/a + y/b = 1 (using integration)

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)

Statement 1 :If the point (2a-5,a^2) is on the same side of the line x+y-3=0 as that of the origin, then a in (2,4) Statement 2 : The points (x_1, y_1)a n d(x_2, y_2) lie on the same or opposite sides of the line a x+b y+c=0, as a x_1+b y_1+c and a x_2+b y_2+c have the same or opposite signs.