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

GRAPHING HELP ASAP!!! TEST TOMORROW!!!!! 4/22/11











































A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectum
x^2-4x-2y=0

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 ASAP!!! TEST TOMORROW!!!!! 4/22/11

Click here to add your own comments

Apr 22, 2011
Graphing Help - Parabola
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
x^2-4x-2y=0

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:

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
To view B), click the following link:

http://www.solving-math-problems.com/graphing-help.html


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

x^2-4x-2y=0

the equation for the standard form of a parabola is:

y = a(x – h)² + k

The general equation is:

y = ax² + bx + c


Convert the equation in A) to standard form:

x² - 4x - 2y = 0

x² - 4x - 2y + 2y = 0 + 2y

x² - 4x + 0 = 0 + 2y

x² - 4x = 0 + 2y

x² - 4x = 2y

2y = x² - 4x

2y/2 = (x² - 4x)/2

y * (2/2) = (x² - 4x)/2

y * (1) = (x² - 4x)/2

y = (x² - 4x)/2

y = x²/2 - 4x/2

y = x²/2 - (4/2)* x

y = x²/2 - (2)* x

y = x²/2 – 2x

y = a(x – h)² + k

the standard form for A) is:

y = a(x – h)² + k

y = (1/2) * (x – 2)² - 2


the vertex is: (h,k)

for this equation, the vertex is: (2,-2)


the focal point of the parabola

focus: (h, k + p)

the conic form of the equation is:

(y - k)² = 4p(x – h)

y = (1/2) * (x – 2)² - 2

y + 2= (1/2) * (x – 2)² - 2 + 2

y + 2= (1/2) * (x – 2)²

(y + 2)*2= 2*(1/2) * (x – 2)²

2*(y + 2) = (x – 2)²

(x – 2)² = 2*(y + 2)

4p = 2

p = ½

focus: (h, k + p) = (2, -2 + ½) = (2, -1.5)


directrix: y = k - p = -2-1/2 = -2.5

latus rectum
the length of the latus rectum = 4p = 4*(1/2) = 2


The parabola 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/parabola-graph.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