Question 1087919
Find the standard form of the equation of the parabola with vertex at (5,2) and focus at (3,2).
<pre>Since the focus: (3, 2) is to the LEFT of the VERTEX (5, 2), this is a PARABOLA with a HORIZONTAL AXIS of SYMMETRY. 
Therefore, the CONIC form of the PARABOLA with a HORIZONTAL AXIS, or {{{(y - k)^2 = 4p(x - h)}}} is used.
h = 5;        k = 2                 p = – 2
{{{(y - k)^2 = 4p(x - h)}}} becomes: 
{{{(y - 2)^2 = 4(- 2)(x - 5)}}}
{{{y^2 - 4y + 4 = - 8x + 40}}} 
{{{8x = - y^2 + 4y + 36}}}
{{{x = (- 1/8)y^2 + (4/8)y + 36/8}}}
{{{highlight_green(matrix(1,3, x, "=", (- 1/8)y^2 + (1/2)y + 9/2))}}} <======== Equation of parabola