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find the equationof he parabola, with vertex at origin, axis of symmetry at x-axis and directrixat x=5

User Nshetty
by
8.7k points

1 Answer

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Explanation:

The equation of parabola if we are interested in the directrix either


(x - h) {}^(2) = 4p(y - k)

or


(y - k) {}^(2) = 4p(x - h)

Since this parabola is symmetric about the x axis, and we have a vertical directrix, we will use the second parabola equation


(y - k) {}^(2) = 4p(x - h)

Here (h,k) is the vertex, so h and k are 0


{y}^(2) = 4px

What is the value of P.

The value of P is the displacement of the vertex to either the focus or directrix.

Since the directrix is right of the vertex, our p will be negative.

The distance between the vertex and directrix is -5.

Long story short: the shortest displacement between a line and a point is the perpendicular dispalcement , which would be -5.


{y}^(2) = 4( - 5)x

Our answer is


{y}^(2) = - 20x

User JTIM
by
8.3k points
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