The parabola `y^2=-12x` rolls without slipping around the parabola `y^2=12x`, The locus of the vertex of rolling `x(x^2 + y^2) + 6lambda y^2=0`, then , `3lambda` is

Consider two parabola y=x^(2)-x+1 and y=x^(2)+x+(1)/(2), the parabola y=-x^(2)+x+(1)/(2) is fixed and parabola y=-x^(2)+1 rolls without slipping around the fixed parabola,then the locus of the focus of the moving parabola is

If x+y=k is a normal to the parabola y^(2)=12x then it touches the parabola

If x+y=k is a normal to the parabola y^(2)=12x then it touches the parabola y^(2)=px then

If x+y+1 = 0 touches the parabola y^(2) = lambda x , then lambda is equal to

The directrix of the parabola y^(2) = 12x, "is " x - 3 .

The parametric equations of the parabola y^(2) = 12x are _

The vertex of the parabola y^(2) - 4y - 16 x - 12 = 0 is

If x+y=k is a normal to the parabola y^(2)=12x, then it touches the parabola y^(2)=px then |P| =