A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then the locus of the focus of the parabola is :

The axis of the parabola y^(2)+2x=0 is

A parabola is drawn through two given points A(1,0,0) and B(-1,0) such that its directrix always touches the circle x^(2)+y^(2)=4. Then The locus of focus of the parabola is=

Let y=x+1 is axis of parabola, y+x-4=0 is tangent of same parabola at its vertex and y=2x+3 is one of its tangents. Then find the focus of the parabola.

If x+y=0,x-y=0 are tangents to a parabola whose focus is (1,2) Then the length of the latusrectum of the parabola is equal

The directrix of a parabola is x+y+4=0 and vertex is at (-1,-1). find the position of the of the focus and the equation of parabola.

A parabola having directrix x +y +2 =0 touches a line 2x +y -5 = 0 at (2,1). Then the semi-latus rectum of the parabola, is

If 2x-y+1=0 is a tangent on the parabola which intersect its directrix at (1,3) and focus is (2,1) ,then equation of axis of parabola 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

Two tangents on a parabola are x-y=0 and x+y=0. S(2,3) is the focus of the parabola. The length of latus rectum of the parabola is