Q10 q2.) find the standard form of the equation of the parabola satisfying the given conditions.

To  solve this problem you must apply the proccedure shown below:

 1. You have that the standard form of the equation of the parabola must satisfy the following conditions given in the exercise above:

 Focus: (-1,4) and Directrix: y=2

 2. Therefore you have:

 √(x0-(-1))²+(y0-4)²=|y0-2|
 (x0+1)²+(y0-4)²=(y0-2)²

 3. When you simplify the expression above and clear y0, you obtain:

 y0=y

 y=1/4(x²+2x+13)
 y=(x²/4)+(x/2)+(13/4)

 Therefore, the answer is: y=(x²/4)+(x/2)+(13/4)