Finding Equation of Axis Aligned Parabolas from given Focal Length and Vertex

1. Given Coordinates of Vertex and a Signed Focal Length, it is possible to find Equations of 2 Axis Aligned Parabolass, one having Directrix Parallel to \(X\)-Axis, and other having Directrix Parallel to \(Y\)-Axis.
2. Given Vertex at a point \((x_v,y_v)\) and a Signed Focal Length \(f\), the Standard Coordinate Equations for Axis Aligned Parabolas are given as
   
   \({(x-x_v)}^2=4f(y-y_v)\)   (For Directrix Parallel to \(X\)-Axis)
   
   \({(y-y_v)}^2=4f(x-x_v)\)   (For Directrix Parallel to \(Y\)-Axis)