   Chapter 12.1, Problem 13E ### 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

# 11-24 Graphing Parabolas An equation of a parabola is given. (a) Find the focus, directrix, and focal diameter of the parabola. (b) Sketch a graph of the parabola and its directrix. y 2 = − 24 x

To determine

To find:

The focus, directrix, and the focal diameter of the parabola.

Explanation

Approach:

The equation of parabola is given by,

y2=4px

And have the following properties.

Vertex =V(0,0).

Focus =F(p,0).

Directrix x=p.

Focal diameter d=|4p|.

Calculation:

Consider the given equation.

y2=24x

Compare the above equation with the equation of parabola.

24x=4pxp=244p=6

The value of p is 6.

The focus of the parabola is given by,

F=(6,0)=(6,0)

The directrix of the parabola is given by,

To determine

(b)

To sketch:

The graph of the parabola and its directrix.

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