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What is an equation of the parabola

What is an equation of the parabola-example-1
User Dan Barron
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1 Answer

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20 votes

Answer:

(c) x = -1/11(y -3)²

Explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

Equation

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Application

Here, we have ...

p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

(h, k) = (0, 3)

so the equation is ...

x = 1/(4(-11/4))(y -3)² +0

x = -1/11(y -3)²

What is an equation of the parabola-example-1
User Sotiris Falieris
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3.1k points