Question 1164212

Find an equation of the parabola with vertex at (2, -4) and directrix x = -5.
<pre>With the DIRECTRIX being “x = ?”, we will have a PARABOLA with a HORIZONTAL AXIS of SYMMETRY (h).
We use the formula for a PARABOLA with a HORIZONTAL AXIS of SYMMETRY: {{{matrix(1,3, (y  -  k)^2, "=", 4p(x  -  h))}}}, where:
                                                                      Vertex is: (h, k) = (2, - 4), and
                                                                      Directrix is:	{{{matrix(6,3, x, "=", h  -  p, - 5, "=", 2  -  p, - 5 - 2, "=", - p, - 7, "=", - p, (- 7)/(- 1), "=", p, 7, "=", p)}}}
{{{matrix(1,3, (y - k)^2, "=", 4p(x - h))}}}
{{{matrix(1,3, (y - - 4)^2, "=", 4(7)(x - 2))}}} ----- Substituting - 4 for k, 7 for p, and 2 for h
{{{highlight_green(matrix(1,5, (y + 4)^2, "=", 28(x - 2), "<======", Equation ))}}}