Find the equation of the parabola whose vertex is at the origin and focus is at the point `(1/(sqrt(2)), 1/(sqrt(2)))`.

Find the equation of the parabola with vertex at (0, 0) and focus is at (0, 2).

Find the focus of the parabola x^2=4y

Find the equation of the parabola with vertex is (2, 1) and the directrix is x = y -1.

Derive the equation of the parabola with its vertex at (3,2) and its focus at (5,2) .

Find the equation of the parabola whose focus is (4,-3) and vertex is (4,-1).

Find the equation of the parabola with vertex at the origin and satisfying the condition : Focus (2, 0) , Directrix x = -2 .

Find the equation of the parabola whose focus is at the point (1,2) and directrix is x+2y+3=0.

Find the equation of the parabola with vertex at the origin and satisfying the condition : Focus (6,0), Directrix x =- 6.

Find the equation of the parabola with vertex at the origin and satisfying the condition : Focus (0, - 3) , Directrix y = 3.

Find the equations of the parabola with vertices at the origin and satisfying the following condition : Focus at (- a, 0).