   Chapter 12.1, Problem 44E ### 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).Focus on the negative y-axis, 6 units away from the directrix.

To determine

To find:

The equation for the parabola that has its vertex at the origin and the focus on the negative y-axis, 6 units away from the directrix.

Explanation

Given:

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(p,0) is as follows.

y2=4px …… (1)

Here, p is the distance from the origin.

The focus is F(p,0) 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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