Find the equation of a hyperbola whose focus is (0,0), directrix is the line x + 2y = 1 and eccentricity is `sqrt(2)`.

Find the equation of the parabola whose focus is (5,3) and directrix is the line 3x-4y+1=0.

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

Find the equation of the hyperbola whose directrix is 2x+y=1, focu s(1,2) and eccentricity sqrt(3)dot

Find the equation of the ellipse whose focus is (1,-1), the corresponding directrix is x-y-3=0, and eccentricity is 1/2 .

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

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

The equation of the parabola with the focus (3,0) and directrix x+3=0 is

Find the equation of the following parabola : Focus at (5,0), Directrix x = - 5.

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