Prove that the straight lines represented by
`(y-mx)^2=a^2 (1+m^2) and (y-nx)^2=a^2(1+n^2)`form rhombus.

Find the equation of the straight lines touching both x^2+y^2=2a^2 and y^2=8a xdot

If the angle between the two lines represented by 2x^2+5x y+3y^2+6x+7y+4=0 is tan^(-1)(m), then find the value of m .

Prove that the line lx+my+n=0 toches the circle (x-a)^(2)+(y-b)^(2)=r^(2) if (al+bm+n)^(2)=r^(2)(l^(2)+m^(2))

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 centres of the circles x^2+y^2=1 , x^2+y^2+6x-2y-1=0 and x^2+y^2-12x+4y=1 are collinear

The lines y = mx , y + 2x = 0 , y = 2x + k and y + mx = k form a rhombus if m equals

Prove that the pair of lines joining the origin to the intersection of the curve (x^2)/(a^2)+(y^2)/(b^2)=1 the line lx+my+n=0 are coincident, if a a^2l^2+b^2m^2=n^2

Find the distance between two Parallel lines : y=mx+c_1 and y=mx+c_2 .

The lines represented by x^(2)+2lambda xy+2y^(2)=0 and the lines represented by (1+lambda)x^(2)-8xy+y^(2)=0 are equally inclined, then lambda =

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)-(y^2)/(b^2)=1, then prove that a^2cos^2alpha-b^2sin^2alpha=p^2dot