The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.
Since we were given Parabola x² = 2 y
Then one has to compare and and so it will be x² = 4 a y
4 a = 2
Make a the subject of the formula:
a = 2/4
= 1/2
Therefore, Focus ( 0,a) = (0, 1/2 )
To solve for directrix:
Note that the equation of the directrix is:
y = -a or y +a=0
Then the equation of the directrix is:
y = - 1/2 or
y = + 1/2 = 0
Then the equation of the directrix will be 2 y +1 =0.
Therefore, The coordinates of the focus and the equation of the directrix is option B: focus: (0, one-half); directrix: y = negative one-half.
See full question below
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
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