MML F/COLLEGE MAT F/TRADES - ACCESS CODE
MML F/COLLEGE MAT F/TRADES - ACCESS CODE
10th Edition
ISBN: 9781323845967
Author: Hobbs
Publisher: PEARSON
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Chapter D, Problem 1RE
To determine

The coordinates of the vertex, focus and the equation of directrix.

Expert Solution
Check Mark

Answer to Problem 1RE

The coordinates of the vertex is (0,0)_, the coordinates of focus is (0,32)_ and the equation of directrix is y=32_.

Explanation of Solution

The given equation is x2=6y.

It is of the standard form x2=4py, whose vertex is at (0,0) and axis at x=0.

The coordinates of the focus is (0,p).

Find the value of p.

p=coefficient of y4=64=32

Therefore, the coordinates of the focus is (0,32).

Standard equation of directrix is y=p.

Hence, for the given equation x2=6y, the equation of directrix is given as follows.

y=p  =(32)=32

Therefore the coordinate of the vertex is (0,0)_, the coordinate of focus is (0,32)_ and the equation of directrix is y=32_.

To determine

To sketch: The parabola and its directrix for the equation x2=6y.

Expert Solution
Check Mark

Explanation of Solution

Procedure used:

To sketch a parabola for an equation in the form x2=4py:

1. Write the given equation in the standard form x2=4py.

2. Calculate the value of p from the formula,

p=coefficient of y4

3. Plot the vertex at (0,0) and focus at (0,p).

4. The directrix y=p is drawn.

5. Substitute the p value for y in the given equation and find two points of x.

6. With vertex at (0,0) sketch the parabola symmetric about yaxis.

Calculation:

The given equation is x2=6y.

From the above part p=32.

Therefore, the coordinate of focus and equation of directrix are (0,32) and y=32_ respectively.

Substitute the value of p=32 for y in the equation x2=6y.

x2=6y=6(32)=9

Taking square root on both sides.

x=+3  or  x=3

Therefore, the points are (3,32) and (3,32).

The parabola and its directrix is sketched as follows:

MML F/COLLEGE MAT F/TRADES - ACCESS CODE, Chapter D, Problem 1RE , additional homework tip  1

From the above graph it is observed that y=32 is the directrix and (0,32) is the focus.

To determine

Whether the given equation is a function or not.

Expert Solution
Check Mark

Answer to Problem 1RE

The given equation x2=6y is a function_.

Explanation of Solution

Procedure used:

To check whether the given equation is a function or not:

1. Plot the graph for the given equation.

2. For the resulting graph, apply the vertical line test.

3. Check whether the vertical line touches the parabola at only one point.

4. If the above condition is true, then the given equation is a function otherwise it is not a function.

Calculation:

The graph for the given equation is drawn as given below.

MML F/COLLEGE MAT F/TRADES - ACCESS CODE, Chapter D, Problem 1RE , additional homework tip  2

From the above figure it is observed that in the vertical line test the vertical line x=3 touches the parabola at only one point.

Therefore, the equation x2=6y is a function_.

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Chapter D Solutions

MML F/COLLEGE MAT F/TRADES - ACCESS CODE

Ch. D.1 - Prob. 11ECh. D.1 - Prob. 12ECh. D.1 - Prob. 13ECh. D.1 - Prob. 14ECh. D.1 - Prob. 15ECh. D.1 - Prob. 16ECh. D.1 - Prob. 17ECh. D.1 - Prob. 18ECh. D.1 - Prob. 19ECh. D.1 - Prob. 20ECh. D.1 - Prob. 21ECh. D.1 - Prob. 22ECh. D.1 - Prob. 23ECh. D.1 - Prob. 24ECh. D.1 - Prob. 25ECh. D.1 - Prob. 26ECh. D.2 - Prob. 1ECh. D.2 - Prob. 2ECh. D.2 - Prob. 3ECh. D.2 - Prob. 4ECh. D.2 - Prob. 5ECh. D.2 - Prob. 6ECh. D.2 - Prob. 7ECh. D.2 - Prob. 8ECh. D.2 - Prob. 9ECh. D.2 - Prob. 10ECh. D.2 - Prob. 11ECh. D.2 - Prob. 12ECh. D.2 - Prob. 13ECh. D.2 - Prob. 14ECh. D.2 - Prob. 15ECh. D.3 - Prob. 1ECh. D.3 - Prob. 2ECh. D.3 - Prob. 3ECh. D.3 - Prob. 4ECh. D.3 - Prob. 5ECh. D.3 - Prob. 6ECh. D.3 - Prob. 7ECh. D.3 - Prob. 8ECh. D.3 - Prob. 9ECh. D.3 - Prob. 10ECh. D.3 - Prob. 11ECh. D.3 - Prob. 12ECh. D.3 - Prob. 13ECh. D.3 - Prob. 14ECh. D.4 - Find the center, the vertices, the foci, and the...Ch. D.4 - Prob. 2ECh. D.4 - Prob. 3ECh. D.4 - Prob. 4ECh. D.4 - Prob. 5ECh. D.4 - Prob. 6ECh. D.4 - Prob. 7ECh. D.4 - Prob. 8ECh. D.4 - Prob. 9ECh. D.4 - Prob. 10ECh. D - Prob. 1RECh. D - Prob. 2RECh. D - Prob. 3RECh. D - Prob. 4RECh. D - Prob. 5RECh. D - Prob. 6RECh. D - Prob. 7RECh. D - Prob. 8RECh. D - Prob. 9RECh. D - Prob. 10RECh. D - Prob. 11RECh. D - Prob. 12RECh. D - Prob. 13RECh. D - Prob. 14RECh. D - Prob. 15RECh. D - Prob. 16RECh. D - Prob. 17RECh. D - Prob. 18RECh. D - Prob. 19RECh. D - Prob. 20RECh. D - Prob. 21RECh. D - Prob. 22RECh. D - Prob. 23RECh. D - Prob. 24RECh. D - Prob. 25RECh. D - Prob. 26RECh. D - Prob. 27RECh. D - Prob. 28RECh. D - Prob. 29RECh. D - Prob. 30RECh. D - Prob. 31RECh. D - Prob. 32RECh. D - Prob. 33RECh. D - Prob. 1PTCh. D - Prob. 2PTCh. D - Prob. 3PTCh. D - Prob. 4PTCh. D - Prob. 5PTCh. D - Prob. 6PTCh. D - Prob. 7PTCh. D - Prob. 8PTCh. D - Prob. 9PTCh. D - Prob. 10PTCh. D - Prob. 11PTCh. D - Prob. 12PTCh. D - Prob. 13PTCh. D - Prob. 14PTCh. D - Prob. 15PTCh. D - Prob. 16PTCh. D - Prob. 17PTCh. D - Prob. 18PTCh. D - Prob. 19PTCh. D - Prob. 20PTCh. D - Prob. 21PTCh. D - Prob. 22PTCh. D - Prob. 23PTCh. D - Prob. 24PTCh. D - Prob. 25PTCh. D - Prob. 26PT
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