If the equation `x^2+(lambda+mu)x y+lambdau y^2+x+muy=0` represents two parallel straight lines, then prove that `lambda=mudot`

9x^(2) +2hxy +4y^(2) +6x +2fy - 3 = 0 represents two parallel lines. Then

Let o lt p lt q and a ne 0 such that the equation px^(2) +4 lambda xy +qy^(2) +4a (x+y +1) = 0 represents a pair of straight lines, then a can lie in the interval

If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 , represents a pair of straight lines, then the value of lambda is

If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k =

Find the value of lambda if 2x^2+7x y+3y^2+8x+14 y+lambda=0 represents a pair of straight lines

If the equations 2x-lambday+5z=7 and lambda x-8y-10z+14=0 represent the same plane then lambda is :

If the equation (5x-1)^2+(5y-2)^2=(lambda^2-2lambda+1)(3x+4y-1)^2 represents an ellipse, then find values of lambdadot

Suppose the circle having equation x^2+y^2=3 intersects the rectangular hyperbola x y=1 at points A ,B ,C ,a n dDdot The equation x^2+y^2-3+lambda(x y-1)=0,lambda in R , represents. (a)a pair of lines through the origin for lambda=-3 (b)an ellipse through A ,B ,C ,a n dD for lambda=-3 (c)a parabola through A , B , C ,a n dD for lambda=-3 (d)a circle for any lambda in R

The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 represent (a)two pairs of perpendicular straight lines (b)two pairs of parallel straight lines (c)two pairs of straight lines which are equally inclined to each other (d)none of these