19. Find the standard form of the equation of the parabola with the given characteristics.
Vertex: ${ }^{(6,3)}$; focus: $(5,3)$

Step 1 ：The standard form of a parabola is given by the equation \((x-h)^2 = 4p(y-k)\) if the parabola opens upwards or downwards, and \((y-k)^2 = 4p(x-h)\) if the parabola opens to the left or right. Here, \((h,k)\) is the vertex of the parabola and \(p\) is the distance from the vertex to the focus.

Step 2 ：In this case, the vertex is given as \((h,k) = (6,3)\) and the focus is \((5,3)\). Since the x-coordinate of the focus is less than the x-coordinate of the vertex, the parabola opens to the left. Therefore, we should use the equation \((y-k)^2 = 4p(x-h)\).

Step 3 ：We can find \(p\) by calculating the distance between the vertex and the focus, which is \(p = h - x_{focus} = 6 - 5 = 1\).

Step 4 ：So, the equation of the parabola is \((y-3)^2 = 4*1*(x-6)\).

Step 5 ：Final Answer: The standard form of the equation of the parabola with vertex at \((6,3)\) and focus at \((5,3)\) is \(\boxed{(y - 3)^2 = 4(x - 6)}\).