logo for solving-math-problems.com
leftimage for solving-math-problems.com

GRAPHING HELP











































A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectum

B) sketch the following ellipse. Indicate on the graph the center,verties, foci and end points of the minor axis
9(x-3)^2+(y+2)^2=9

Comments for GRAPHING HELP

Click here to add your own comments

Apr 20, 2011
Graphing an Ellipse
by: Staff


The question:

A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectum

B) sketch the following ellipse. Indicate on the graph the center,verties, foci and end points of the minor axis
9(x-3)^2+(y+2)^2=9


The answer:

A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectum

You forgot to include the parabola, so we are unable to answer the question for A).



B) sketch the following ellipse. Indicate on the graph the center, vertices, foci and end points of the minor axis



9(x-3)² + (y+2)² = 9

The general equation for an ellipse is:

(x-h)²/a² + (y-k)²/b² = 1

2*a and 2*b are the lengths of the x and y axis of the ellipse

To rewrite equation in standard format, divide each side of the equation by 9

9(x-3)²/9 + (y+2)²/9 = 9/9

(x-3)²/1 + (y+2)²/9 = 1

(x-3)²/1² + (y+2)²/3²=1

a² = 1²
a = 1
length of x axis of the ellipse = 2*a = 2*1 = 2

b² = 3²
b = 3
length of y axis of the ellipse = 2*b = 2*3 = 6


Calculation of the center of the ellipse:

x - 3 = 0
x = 3

y + 2 = 0
y = -2

the center of the ellipse: x = 3, y = -2


Calculation of the vertices of the ellipse for the x and y axes

x (end points of axis) = (x value at center) ± a

x = 3 ± 1

x = 2
x = 4

y (end points of axis) = (y value at center) ± b

y = -2 ± 3

y = 1
y = -5


End points:

x axis (minor axis), vertices
(2,-2 ), (4,-2)

y axis (major axis), vertices
(3,1 ), (3,-5)


Graph:

Since we now know the coordinates for the center of the ellipse, and the vertices for both the x axis and the y axis, we can sketch the ellipse:

The ellipse is shown in the following graph (click link to view, use the Backspace key to return to this page):

http://www.solving-math-problems.com/images/ellipse-graphing-help-2011-04-19.png


Calculation of foci

The foci lie on the major axis

If b > a, then

c² = b² - a²

If a > b, then

c² = a² - b²


Since b > a

c² = 3² - 1²

c² = 9 – 1

c² = 8

c = √8

c = ± 2.82842712

The foci are:

(3, -2 ± 2.82842712)
(3, -4.83), (3, 0.83)

Graph:

The foci can now be added to the sketch of the ellipse:

(click link to view, use the Backspace key to return to this page):

http://www.solving-math-problems.com/images/ellipse-with-foci-graphing-help-2011-04-19.png



Thanks for writing.


Staff
www.solving-math-problems.com



Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com