   Chapter 12.1, Problem 47E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### 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 has y-intercept 6 .

To determine

To find:

The equation for the parabola that has its vertex at the origin and the directrix has y-intercept 6.

Explanation

Given:

The vertex is V(0,0).

Approach:

The general equation for a parabola with a vertical 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 x=p

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

Calculation:

Since, the vertex of the parabola lies halfway between the focus and the directrix.

The figure is plotted as given below.

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