Write an equation of a parabola with vertex at the origin and the given focus.

Question

focus ​(7​,0)
Question content area bottom
Part 1
What is the correct​ equation?
A.y squared equals negative 28 x
y squared equals negative 28 x
B.y equals 28 x squared
y equals 28 x squared
C.x equals one seventh y squared
x equals one seventh y squared
D.x equals StartFraction 1 Over 28 EndFraction y squared
x equals StartFraction 1 Over 28 EndFraction y squared

Answer 1

The correct equation of a parabola with the vertex at the origin and a focus at (7,0) is:
(x - 7)^2 = 4p(y)

Since the vertex is at the origin, the equation simplifies to:
x^2 = 4p(y)

Since the focus is at (7,0), the distance from the focus to the vertex is p = 7. Therefore, the equation becomes:
x^2 = 28y

So, the correct answer is:
A. y squared equals negative 28 x