Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4?

x2=−8(y−2)
x2=−2y
x2=−8y
x2=−2(y−2)

x2=−8(y−2)

Step-by-step explanation:

Parabola is a locus of a point which moves at the same distance from a fixed point called the focus and a given line called the directrix.

Let P(x,y) be the moving point on the parabola with  

focus at S(h,k)= S(0,0)  

& directrix at y= 4

Now,  

|PS| = √(x-h)2 + (y-k)2

|PS| = √(x-0)2 + (y-0)2

|PS| = √ x2 + y2

Let ‘d’ be the distance of the moving point P(x,y) to directrix y- 4=0

equation of parabola is:  

Squaring on both sides, we get:  

This is the required equation of the parabola with focus at (0,0) and directrix at y= 4.

I just took the test and it was x^2=-8(y-2)

Step-by-step explanation:

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step-by-step explanation:

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