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Deffense [45]
3 years ago
7

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
Mathematics
1 answer:
Airida [17]3 years ago
6 0

Answer:

b)

<em>i) Focus ( 0,a) = </em>(0,\frac{1}{2} )<em></em>

<em>ii) The equation of the directrix is </em>

<em>                             </em>y = -\frac{1}{2}  or y +\frac{1}{2} =0

Step-by-step explanation:

<u>Step(i)</u>:-

  <em> </em><em> 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 </em>

<em>• The Fixed line is called the directrix of the parabola. </em>

<em>• The Fixed point is called the focus of the parabola. </em>

<em>• A line through the focus and perpendicular to the directrix is called the axis of the parabola. </em>

<em>• The point of intersection of parabola with the axis is called the vertex of the parabola. </em>

<em>Given Parabola x² = 2 y</em>

<em>Comparing  x² = 4 a y</em>

<em>                    4 a = 2</em>

<em>                      </em>a = \frac{1}{2}<em></em>

<em>   Focus ( 0,a) = </em>(0,\frac{1}{2} )<em></em>

<u><em>Step(ii)</em></u>

<em>The equation of the directrix is y = -a or y +a=0</em>

<em>The equation of the directrix is </em>

<em>                             </em>y = -\frac{1}{2}  or y +\frac{1}{2} =0<em></em>

<em>The equation of the directrix is 2 y +1 =0</em>

<em> </em>

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