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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: ; directrix: y = focus: (8,0); directrix: x = –8 focus: ; directrix: x =

Respuesta :

Answer:

the coordinate of the focus is: (0, 1/2)

the equation of the directrix is: y=-1/2

Step-by-step explanation: The standard equation for a parabola that opens upward- parallel to the y-axis, is: x2=4ay. Meaning, a = distance from the vertex to focus and the vertex is at origin: (0,0).

4a is equal to 2

a is equal to 2/4

a is equal to 1/2 or 0.5

varshamittal029

The parabola has

focus: (0,1/2)

directix: y=-1/2

What is the formula for focus and directrix of a parabola?

If the parabola is given by

y=a(x-h)²+k

then the focus of the parabola is given by

(h,k+1/4a)

and the directrix of the parabola is given by

y=k-a

How to solve the problem?

Given parabola is x²=2y

So, the parabola is y=(1/2)x², when compared with y=a(x-h)²+k  we have

a=1/2, h=0 and k=0

So, the focus of the parabola is

[tex](0,\frac{1}{4\frac{1}{2}})= (0,\frac{1}{2})[/tex]

and, the directrix of the parabola is

y= -1/2.

Hence, the parabola has

focus: (0,1/2)

directix: y=-1/2

To learn more about parabola visit- https://brainly.com/question/4074088?referrer=searchResults

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