Question 1028313
You can derive the equation for your question #1 using Distance Formula and the given focus and directrix and the written definition of a parabola.  The previous referenced videos show how that is done.  


Your question number 2 is basically in standard form and shows y as a function of x, and since coefficients are positive, this parabola has a vertex minimum and graph is concave upward.  The way the equation is shown corresponds to {{{x^2=4py}}}, which can also be expanded to  {{{(x-0)^2=12(y-0)}}}, telling you that  vertex is at the origin, and you find p from {{{12=4p}}}; and knowing p will give you information to find the focus and the directrix.