Write an equation of a parabola with vertex at the origin and the given focus.
focus (8,0)
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Part 1
What is the correct equation?
A.y squared equals negative 32 x
y squared equals negative 32 x
B.x equals StartFraction 1 Over 32 EndFraction y squared
x equals StartFraction 1 Over 32 EndFraction y squared
C.x equals one eighth y squared
x equals one eighth y squared
D.y equals 32 x squared
y equals 32 x squared
Since the focus is at (8,0) and the vertex is at the origin, we know that the focal length is equal to the x-coordinate of the focus, which is 8.
The equation of a parabola with vertex at the origin and focal length of 8 is of the form x = a*y^2.
Substitute the focus coordinates into the equation x = a*y^2:
8 = a*0^2
a = 8
Therefore, the correct equation is x = 8y^2.
Answer: x = 8y^2