If `x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl - m^(2)) `, then show that ` lx + my + nz = 0`.

If x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl-m^(2)) , then prove that lx + my + nz = 0 .

If x/(lm - n^2) = y/(mn - l^2) = z/(nl - m^2) the value of lx + my +nz will be

If a^(x)=m,a^(y)=n and a^(2)=(m^(y)n^(x))^(z) show that xyz=1

If the line (x-3)/(2) = (y + 2)/(-1) = (z +4)/(3) lies in the plane lx + my -z = 9 , then l^(2) + m^(2) is equal to

Find the equation of a circle circumscribing the triangle whose sides are x=0 , y=0 and lx +my =1. If l, m vary so that l^(2) + m^(2) = 4l^(2)m^(2) , find the locus of the centre of the circle.

Let's find value of : a (m + n) + b ( n + l) + c(l + m) if a = lx + my +n, b = mx + ny +l, c = nx + ly +m

If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , show that a^(2) l^(2)-b^(2)m^(2)=n^(2) .

If 7l^2 - 9m^2 + 8l + 1 = 0 and we have to find equation of circle having lx + my + 1 = 0 is a tangent and we can adjust given condition as 16l^2 + 8l + 1 = 9(l^2 + m^2) or (4l^2 + 1)^2 = 9(l^2 + m^2) implies |4l + 1|/sqrt ((l^2 + m^2)) = 3 Centre of circle = (4, 0) and radius = 3 when any two non parallel lines touching a circle, then centre of circle lies on angle bisector of lines. Answer the following question based on above passage : If 16m^2 - 8l - 1 = 0 , then equation of the circle having lx + my + 1 = 0 is a tangent is

If tan^(2)z= tan (x+y) tan (x-y) , show that cot^(2)y+ cot (z+x) cot (z-x)=0

If z=x+iy is a complex number with x, y in Q and |z| = 1 , then show that |z^(2n)-1| is a rational numberfor every n in N .