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High School Math Calculus PRECALCULUS:GRAPHICAL,...-NASTA ED.

a. To graph : The coordinate axes in the construction window. Given information: Two the name of axis x & y . Graph: Interpretation: Draw/display the coordinate axes (Graph >> Define Coordinate System ) as shown: b. To graph: The line y = − 1 as the directrix and the point 0 , 1 as the focus. Given information: Line y = − 1 . The point 0 , 1 . Graph: Interpretation: Plot point 0 , 1 which named F and the line y = − 1 . c. To graph : The horizontal lines and concentric circle. Given information: Horizontal line. Concentric circle. Graph: Interpretation: The center of the concentric circles is 0 , 1 or point F in our case. The Snap Points feature will be helpful in constructing the concentric circles and the horizontal lines as shown d. To graph : The points where these horizontal lines and concentric circles meet. Given information: Construct the points where these horizontal lines and concentric circles meet. Graph: Interpretation: Construct the points where these horizontal lines and concentric circles meet . e. To prove: The points lie on the parabola with directrix y = − 1 and focus 0 , 1 . Given information: The point which is needed to be verified if it lies on the parabola with directrix y = − 1 and focus 0 , 1 . Proof: A parabola with directrix y = − 1 and focus at ( 0 , 1 ) has equation x 2 = 4 y . Since P is on the circle x 2 + ( y − 1 ) 2 = n 2 and on the line y = n − 1 , its x -coordinate of P must be x = n 2 − ( ( n − 1 ) − 1 ) 2 = n 2 − ( n − 2 ) 2 Substituting n 2 − ( n − 2 ) 2 , n − 1 into x 2 = 4 y shows that n 2 − ( n − 2 ) 2 2 = 4 ( n − 1 ) where P lies on the parabola x 2 = 4 y

a. To graph : The coordinate axes in the construction window. Given information: Two the name of axis x & y . Graph: Interpretation: Draw/display the coordinate axes (Graph >> Define Coordinate System ) as shown: b. To graph: The line y = − 1 as the directrix and the point 0 , 1 as the focus. Given information: Line y = − 1 . The point 0 , 1 . Graph: Interpretation: Plot point 0 , 1 which named F and the line y = − 1 . c. To graph : The horizontal lines and concentric circle. Given information: Horizontal line. Concentric circle. Graph: Interpretation: The center of the concentric circles is 0 , 1 or point F in our case. The Snap Points feature will be helpful in constructing the concentric circles and the horizontal lines as shown d. To graph : The points where these horizontal lines and concentric circles meet. Given information: Construct the points where these horizontal lines and concentric circles meet. Graph: Interpretation: Construct the points where these horizontal lines and concentric circles meet . e. To prove: The points lie on the parabola with directrix y = − 1 and focus 0 , 1 . Given information: The point which is needed to be verified if it lies on the parabola with directrix y = − 1 and focus 0 , 1 . Proof: A parabola with directrix y = − 1 and focus at ( 0 , 1 ) has equation x 2 = 4 y . Since P is on the circle x 2 + ( y − 1 ) 2 = n 2 and on the line y = n − 1 , its x -coordinate of P must be x = n 2 − ( ( n − 1 ) − 1 ) 2 = n 2 − ( n − 2 ) 2 Substituting n 2 − ( n − 2 ) 2 , n − 1 into x 2 = 4 y shows that n 2 − ( n − 2 ) 2 2 = 4 ( n − 1 ) where P lies on the parabola x 2 = 4 y

PRECALCULUS:GRAPHICAL,...-NASTA ED.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

See similar textbooks

Expert Solution & Answer

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 8.1, Problem 72E

Solution

a.

To graph: The coordinate axes in the construction window.

Given information:

Two the name of axis $x & y$ .

Graph:

Interpretation:

Draw/display the coordinate axes (Graph >> Define Coordinate System) as shown:

b.

To graph: The line $y=−1$ as the directrix and the point $0,1$ as the focus.

Given information:

Line $y=−1$ .

The point $0,1$ .

Graph:

Interpretation:

Plot point $0,1$ which named $F$ and the line $y=−1$ .

c.

To graph: The horizontal lines and concentric circle.

Given information:

Horizontal line.

Concentric circle.

Graph:

Interpretation:

The center of the concentric circles is $0,1$ or point $F$ in our case.

The Snap Points feature will be helpful in constructing the concentric circles and the horizontal lines as shown

d.

To graph: The points where these horizontal lines and concentric circles meet.

Given information:

Construct the points where these horizontal lines and concentric circles meet.

Graph:

Interpretation:

Construct the points where these horizontal lines and concentric circles meet .

e.

To prove: The points lie on the parabola with directrix $y=−1$ and focus $0,1$ .

Given information:

The point which is needed to be verified if it lies on the parabola with directrix $y=−1$ and focus $0,1$ .

Proof:

A parabola with directrix $y=−1$ and focus at $(0,1)$ has equation $x2=4y$ . Since $P$ is on the circle $x2+(y−$ $1)2=n2$ and on the line $y=n−1$ , its $x$ -coordinate of $P$ must be

$x=n2−((n−1)−1)2=n2−(n−2)2$

Substituting $n2−(n−2)2,n−1$ into $x2=4y$ shows that $n2−(n−2)22=4(n−1)$ where $P$ lies on the parabola $x2=4y$

Chapter 8.1, Problem 71E

Chapter 8.1, Problem 73E

Chapter 8 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 8.1 - Prob. 1QR Ch. 8.1 - Prob. 2QR Ch. 8.1 - Prob. 3QR Ch. 8.1 - Prob. 4QR Ch. 8.1 - Prob. 5QR Ch. 8.1 - Prob. 6QR Ch. 8.1 - Prob. 7QR Ch. 8.1 - Prob. 8QR Ch. 8.1 - Prob. 9QR Ch. 8.1 - Prob. 10QR

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - 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Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.2 - Prob. 59E Ch. 8.2 - Prob. 60E Ch. 8.2 - Prob. 61E Ch. 8.2 - Prob. 62E Ch. 8.2 - Prob. 63E Ch. 8.2 - Prob. 64E Ch. 8.2 - Prob. 65E Ch. 8.2 - Prob. 66E Ch. 8.2 - Prob. 67E Ch. 8.2 - Prob. 68E Ch. 8.2 - Prob. 69E Ch. 8.2 - Prob. 70E Ch. 8.2 - Prob. 71E Ch. 8.2 - Prob. 72E Ch. 8.2 - Prob. 73E Ch. 8.2 - Prob. 74E Ch. 8.2 - Prob. 75E Ch. 8.2 - Prob. 76E Ch. 8.3 - Prob. 1QR Ch. 8.3 - Prob. 2QR Ch. 8.3 - Prob. 3QR Ch. 8.3 - Prob. 4QR Ch. 8.3 - Prob. 5QR Ch. 8.3 - Prob. 6QR Ch. 8.3 - Prob. 7QR Ch. 8.3 - Prob. 8QR Ch. 8.3 - Prob. 9QR Ch. 8.3 - Prob. 10QR Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Prob. 40E Ch. 8.3 - Prob. 41E Ch. 8.3 - Prob. 42E Ch. 8.3 - Prob. 43E Ch. 8.3 - Prob. 44E Ch. 8.3 - Prob. 45E Ch. 8.3 - Prob. 46E Ch. 8.3 - Prob. 47E Ch. 8.3 - Prob. 48E Ch. 8.3 - Prob. 49E Ch. 8.3 - Prob. 50E Ch. 8.3 - Prob. 51E Ch. 8.3 - Prob. 52E Ch. 8.3 - Prob. 53E Ch. 8.3 - Prob. 54E Ch. 8.3 - Prob. 55E Ch. 8.3 - Prob. 56E Ch. 8.3 - Prob. 57E Ch. 8.3 - Prob. 58E Ch. 8.3 - Prob. 59E Ch. 8.3 - Prob. 60E Ch. 8.3 - Prob. 61E Ch. 8.3 - Prob. 62E Ch. 8.3 - Prob. 63E Ch. 8.3 - Prob. 64E Ch. 8.3 - Prob. 65E Ch. 8.3 - Prob. 66E Ch. 8.3 - Prob. 67E Ch. 8.3 - Prob. 68E Ch. 8.3 - Prob. 69E Ch. 8.3 - Prob. 70E Ch. 8.3 - Prob. 71E Ch. 8.3 - Prob. 72E Ch. 8.3 - Prob. 73E Ch. 8.3 - Prob. 74E Ch. 8.3 - Prob. 75E Ch. 8.4 - Prob. 1QR Ch. 8.4 - Prob. 2QR Ch. 8.4 - Prob. 3QR Ch. 8.4 - Prob. 4QR Ch. 8.4 - Prob. 5QR Ch. 8.4 - Prob. 6QR Ch. 8.4 - Prob. 7QR Ch. 8.4 - Prob. 8QR Ch. 8.4 - Prob. 9QR Ch. 8.4 - Prob. 10QR Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - 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Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Prob. 24E Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.6 - Prob. 35E Ch. 8.6 - Prob. 36E Ch. 8.6 - Prob. 37E Ch. 8.6 - Prob. 38E Ch. 8.6 - Prob. 39E Ch. 8.6 - Prob. 40E Ch. 8.6 - Prob. 41E Ch. 8.6 - Prob. 42E Ch. 8.6 - Prob. 43E Ch. 8.6 - Prob. 44E Ch. 8.6 - Prob. 45E Ch. 8.6 - Prob. 46E Ch. 8.6 - Prob. 47E Ch. 8.6 - Prob. 48E Ch. 8.6 - Prob. 49E Ch. 8.6 - Prob. 50E Ch. 8.6 - Prob. 51E Ch. 8.6 - 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