x=0 represents the equation of

If lambda x^(2) + 4xy + y^(2) + lambda x + 3y + 2 = 0 represents the equation of the parabola , then the vlaue of lambda is _

If (2x + 3y + 1) + lambda ( x - 2y - 3) = 0 represents the equation of a horizontal line , then find the value of lambda .

If H(x,y)=0 represents the equation of a hyperbola and A(x,y)=0 , C(x,y)=0 the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point (alpha, beta) in the plane H(alpha,beta) , A(alpha,beta) , and C(alpha,beta) are in

If H(x,y)=0 represents the equation of a hyperbola and A(x,y)=0 , C(x,y)=0 the joint equation of its asymptotes and the conjugate hyperbola respectively, then for any point (alpha, beta) in the plane H(alpha,beta) , A(alpha,beta) , and C(alpha,beta) are in

Show that the equation 9x^(2) - 16y^(2) - 18x - 64y - 199 = 0 represents the equation of a hyperbola, find the coordinates of its centre and foci and also the equations of its directrices

If 3x+4y+k=0 represents the equation of tangent at the vertex of the parabola 16x^(2)-24xy+9y^2+14x+2y+7=0 , then the value of k is ________ .

If 3x+4y+k=0 represents the equation of tangent at the vertex of the parabola 16x^(2)-24xy^(2)+14x+2y+7=0 , then the value of k is ________ .

If 3x+4y+k=0 represents the equation of tangent at the vertex of the parabola 16x^(2)-24xy^(2)+14x+2y+7=0 , then the value of k is ________ .