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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

31-48 Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and satisfies the given condition(s).

Directrix: y = 1 2

To determine

To find:

The equation for the parabola that has its vertex at the origin and the directrix is y=12.

Explanation

Given:

The directrix is y=12 and the vertex is V(0,0).

Approach:

The general equation for a parabola with a horizontal axis having the vertex at the origin and the focus F(0,p) is as follows.

x2=4py …… (1)

Here, p is the distance from the origin.

The focus is F(0,p) and the directrix line is y=p

The parabola opens to the right, if p>0 or to the left if p<0.

Calculation:

The directrix of a parabola is y=12

It is in the form of the directrix line is y=p.

Compare the value of x above two expressions. Then,

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Chapter 12 Solutions

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