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

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