Find the vertex of the parabola `x^2=2(2x+y)`

Find the area of the triangle found by the lines joining the vertex of the parabola x^(2) -36y to the ends of the latus rectum.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = 12y to the ends of its latus rectum.

The vertex of the parabola y^2 = 4x + 4y 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 ________ .

The vertex of the parabola x^(2)=8y-1 is :

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

Find the angle made by a double ordinate of length 2a at the vertex of the parabola y^(2)=ax .

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4(x+1), then prove that 2(a+1)=b^2

The vertex of the parabola y^2 + 4x = 0 is

Find the length of normal chord which subtends an angle of 90^0 at the vertex of the parabola y^2=4xdot