Answer:
[tex](x+4)^2=28(y-3)[/tex]
Step-by-step explanation:
The directrix of the parabola is the horizontal line with the eqaution [tex]y=-4.[/tex] The focus of the parabola is at point (-4,10), than the axis of symmetry of the parabola is the perpendicular line to the directrix passing through the focus. Its equation is [tex]x=-4[/tex]
The distance between the directrix and the focus is [tex]|10-(-4)|=14,[/tex] so [tex]p=14[/tex] and the vertex is at point [tex]\left(-4,10-\dfrac{14}{2}\right)\rightarrow (-4,3)[/tex]
Parabola goes in positive y-direction, hence its equation is
[tex](x-x_0)^2=2p(y-y_0),[/tex]
where [tex](x_0,y_0)[/tex] is the vertex, so the equation of this parabola is
[tex](x+4)^2=28(y-3)[/tex]
