Finding Parameters of Axis Aligned Parabola from Standard Coordinate Equation

1. As given in the Derivation of Standard and Explicit Coordinate Equations for Axis Aligned Parabolas, the Standard Coordinate Equation for Axis Aligned Parabolas is given as
   
   \({(x-x_v)}^2 = 4f(y-y_v)\)   (For Parabolas having Directrix Parallel to \(X\)-Axis)...(1)
   
   \({(y-y_v)}^2 = 4f(x-x_v)\)   (For Parabolas having Directrix Parallel to \(Y\)-Axis)...(2)
   
   In equation (1) the Variable \(x\) has the Quadratic Term. In equation (2) the Variable \(y\) has the Quadratic Term.
   
   In equation (1) Variable \(y\) has only the Linear Term. In equation (2) Variable \(x\) has only the Linear Term. These Variables will be refered to as Variable with Only Linear Term (VLT) below.
   
   Please notice that in both equations (1) and (2) the Co-efficient of the VLT is 4 times the Signed Focal Length \(f\).
2. The following gives the Formulae for finding out Various Parameters of Parabola given the Standard Equation
   1. Coordinates of the Vertex: \((-x_v,-y_v)\)
   2. Signed Focal Length \(f\) : \(\frac{(Co-efficient\hspace{.2cm}of\hspace{.2cm}VLT)}{4}\)
   3. Length for Latus Rectum : |Co-efficient of VLT|=\(|4f|\)
   4. If Directrix is Parallel to \(X\)-Axis then
      Coordinate of the Focus: \((-x_v,-y_v+f)\)
      Coordinates of Points of Intersection of Latus Rectum and Parabola: \((-x_v-2f,-y_v+f)\),\((-x_v+2f,-y_v+f)\)
      Equation of Directrix: \(y=-y_v-f\)
      Equation of Base: \(y=-y_v\)
      Equation of Latus Rectum: \(y=-y_v+f\)
      Equation of Axis of Symmetry: \(x=-x_v\)
      
   5. If Directrix is Parallel to \(Y\)-Axis then
      Coordinate of the Focus: \((-x_v+f,-y_v)\)
      Coordinates of Points of Intersection of Latus Rectum and Parabola: \((-x_v+f,-y_v-2f)\),\((-x_v+f,-y_v+2f)\)
      Equation of Directrix: \(x=-x_v-f\)
      Equation of Base: \(x=-x_v\)
      Equation of Latus Rectum: \(x=-x_v+f\)
      Equation of Axis of Symmetry: \(y=-y_v\)