Respuesta :
Answer:
b)
i) Focus ( 0,a) = [tex](0,\frac{1}{2} )[/tex]
ii) The equation of the directrix is
[tex]y = -\frac{1}{2} or y +\frac{1}{2} =0[/tex]
Step-by-step explanation:
Step(i):-
A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane
• The Fixed line is called the directrix of the parabola.
• The Fixed point is called the focus of the parabola.
• A line through the focus and perpendicular to the directrix is called the axis of the parabola.
• The point of intersection of parabola with the axis is called the vertex of the parabola.
Given Parabola x² = 2 y
Comparing x² = 4 a y
4 a = 2
[tex]a = \frac{1}{2}[/tex]
Focus ( 0,a) = [tex](0,\frac{1}{2} )[/tex]
Step(ii)
The equation of the directrix is y = -a or y +a=0
The equation of the directrix is
[tex]y = -\frac{1}{2} or y +\frac{1}{2} =0[/tex]
The equation of the directrix is 2 y +1 =0
