If the family of lines `lambdax + 3y - 6 = 0 (lambda` is variable) intersect the lines `x - 2y + 3 = 0 and x-y + 1 = 0` in P and Q, then locus of the middle point of PQ is

If the family of lines lambda x+3y-6=0(lambda is variable) intersect the lines x-2y+3=0 and x-y+1=0 in P and Q,then locus of the middle point of PQ is

y = mx be a variable line (m is variable) intersect the lines 2x + y-2=0 and x-2y + 2 = 0 in P and Q.The locus of midpoint of segment of PQ is

A member of the family of lines (x+ y -1) + lambda(2x +3y-2) =0, lambda in R intersects a member of the family of lines (ax+y-2) + alpha(bx + 4y-5) = 0, alpha in R , at a fixed point. The ordered pair (a, b) is

Line 2x - 3y + 8 = 0 intersects parabola y^(2) = 8x of points P and Q then point of bar(PQ) is ……..

The tangent at a variable point P of the curve y=x^(2)x^(3) meets it again at Q. Show that the locus of the middle point of PQ is y=1-9x+28x^(2)-28x^(3)

For the variable t, the locus of the point of intersection of the lines 3 tx - 2y + 6t = 0 and 3x + 2ty - 6 = 0 is _

A member of the family of lines (x+y-1)+lambda(2x+3y-2)=0,lambda in R intersects a member of the family of lines (ax+y-2)+alpha(bx+4y-5)=0,alpha in R at a fixed point.The ordered pair (a,b) is

The lines x+3y-1=0 and x-4y=0 intersect each other. Find their point of intersection.