SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} \text{directrix}=x=-4 \\ \text{Focus:}(2,4) \end{gathered}[/tex]
STEP 2: Write the equation of a parabola
[tex]\begin{gathered} \text{The equation is given as:} \\ x=\frac{1}{4(f-h)}(y-k)^2+h\text{ where} \\ (h,k)\text{ is the vertex} \\ (f,k)is\text{ the focus} \\ \text{Thus,} \\ f=2,k=4 \end{gathered}[/tex]
STEP 3: Get the value of h
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix. Therefore:
[tex]\begin{gathered} f-h=h-(-4) \\ By\text{ substitution}, \\ 2-h=h+4 \\ 2-4=h+h \\ -2=2h \\ h=-\frac{2}{2}=-1 \end{gathered}[/tex]
STEP 4: Get the standard form of equation
Hence, the standard form becomes:
[tex]\begin{gathered} \text{The standard form is given as:} \\ x=\frac{y^2}{12}-\frac{2y}{3}+\frac{1}{3} \end{gathered}[/tex]
