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Find an equation for the parabola that has its vertex at the origin and has its focus at the point: ( − 7.32 , 0 ) .

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Explanation:

1.What is the equation of a parabola with a vertex at (0, 0)?

y = ax²; y = -ax²; x = ay²; x = -ay² where a = [½, 1 , 2]

Also an infinity of others at various values of a and various angles.

2.The focus lies above the vertex, so the parabola is vertical and the focal length p=10.25

Equation for up-opening parabola with vertex (h,k) and focal length p:

y=14p(x−h)2+k

y=14p(x−0)2+0y=141x2

3.Since the directrix is the line y=−10.25 , a point (x,y) is on the parabola if, and only if,

x2+(y−10.25)2=(y+10.25)2.

Therefore, x2−20.5y=20.5y and y=141x2.

hope I helped

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