A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix? focus: (0,8); directrix: y = –8 focus: (0, one-half); directrix: y = negative one-half focus: (8,0); directrix: x = –8 focus: (one-half, 0); directrix: x = negative one-half

b)

i) Focus ( 0,a) =

ii) The equation of the directrix is

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

  Focus ( 0,a) =

Step(ii)

The equation of the directrix is y = -a or y +a=0

The equation of the directrix is

The equation of the directrix is 2 y +1 =0

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step-by-step explanation: