   Chapter 12.1, Problem 3E ### 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

# The graph of the equation y 2 = 4 p x is the parabola with focus F ( _ _ , _ _ ) and directix x = _____. So the graph of y 2 = 12 x is a parabola with focus F ( _ _ , _ _ ) and the directrix x = _____.

To determine

To fill:

The blank in the given statement, “The graph of the equation y2=4px is the parabola with focus F(__,__) and directix x=_____. So the graph of y2=12x is a parabola with focus F(__,__) and the directrix x=_____.”

Explanation

Given:

The equation is given as,

y2=12x

Approach:

The equation of a parabola is given by,

y2=4px… (1)

And, the properties for the parabola are as follows,

Vertex =V(0,0).

Focus =F(p,0).

Directrix x=p.

Calculation:

Consider the given equation.

y2=12x

Compare the above equation with the equation (1).

12x=4pxp=124p=3

The value of p is 3.

The focus of the parabola is,

F=(3,0)

The directrix of the parabola is,

x=3

Therefore, the complete statement after filling the blanks is “The graph of the equation y2=4px is the parabola with focus F(p,0)_ and directrix x=p_

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