Write the standard form equation for each parabola

Question

Vertex (6 , -10) and focus (23/4 , -10)

Answer 1

The vertex (h,k) and focus both lie on the axis of the parabola.  So, the axis is horizontal.  

 

Equation of parabola: (y-k)² = 4p(x-h)

 

                               (y+10)² = 4p(x-6))

 

                              Since the focus lies 1/4 unit left of the vertex, the parabola opens leftward and                                         p = -1/4.

 

                              So, the equation of the parabola is

                                  (y+10)² = -(x-6).