Explanation Given: The equation is given as, y 2 = 12 x Approach: The equation of a parabola is given by, y 2 = 4 p x … (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. y 2 = 12 x Compare the above equation with the equation (1). 12 x = 4 p x p = 12 4 p = 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 y 2 = 4 p x is the parabola with focus F ( p , 0 ) _ and directrix x = − p _

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 12.1, Problem 3E

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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=_.”

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Chapter 12.1, Problem 2E

Chapter 12.1, Problem 4E

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Chapter 12 Solutions

Algebra and Trigonometry (MindTap Course List)

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The blank in the given statement, “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 = _.”

Solution Summary: The author explains that the graph of the equation y2=12x is a parabola with focus F(p,0) and directrix

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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=_.”

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Chapter 12 Solutions

The blank in the given statement, “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 = _____.”

Solution Summary: The author explains that the graph of the equation y2=12x is a parabola with focus F(p,0) and directrix

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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=_____.”

Want to see the full answer?

Chapter 12 Solutions

The blank in the given statement, “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 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=_.”