if the line 2x + 3y + 4 + `lambda`(6x-y+12)=0 passes through the point (1,2), find the value of `lambda`.

If the angle theta between the line (x+1)/(1) = ( y-1)/(2) = (z-2)/(2) and the plane 2x-y+sqrt( lambda ) z + 4 =0 is such that sin theta = (1)/(3) then the value of lambda is

The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=0 . The third side, which is variable, always passes through the point (-5,-1) . Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then

Find the general equation of the line which is parallel to 3x-4y+5 = 0 . And such that line passes through the point (-1,2)

Find the equation of the line parallel to the line 3x- 4y + 2 = 0 and passing through the point (- 2, 5).

Fill ups If the lines (x-1)/2=(y+2)/-3=(z-4)/lambda and x/1=y/-2=z/2 are t right angles then the value of lambda is……………

Find equation of the line parallel to the line 3x-4y+ 2=0 and passing through the point (-2, 3).

A horizontal plane 4x-3y+7z=0 is given. Find a line of greatest slope passes through the point (2, 1, 1) in the plane 2x+y-5z=0 .

The equation x^(2)+2xy+4=0 is transformed to the parallel axes through the point (6, lambda) . For what value of lambda its new form passes through the new origin ?