Friday, October 17, 2008

MYP Algebra 2 - Ch10 - Error Analysis 2

p.612 #4
What did the student do wrong? What is the correct equation?
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7 comments:

Anonymous said...

For an ellipse with a horizontal major axis, the standard form of the equation is (x^2/a^2) + (y^2/b^2)=1, where a represents the distance from the origin of the vertices and b represents the distance from the origin for the co-vertices. In the ellipse, the vertices are 3 units from the origin and the co-vertices are 2 units from the origin. The standard form of the equation for this ellipse would be (x^2/9) + (y^2/4) =1.

4:39 PM
Anonymous said...

According to the standard form of an equation with a major axis that is horizontal , the equation of an ellipse is (x^2/a^2)+(y^2/b^2)=1 . The verticies can be located at (a ,0) and (-a,0< , whereas the co-verticies can be located at (0,b) and (0,-b). According to the graph on p.612 for number 12, the student confussed the verticies from the co-verticies. The verticies are 3 units to the left and right of the origion[(0,0)], and the co-verticies are 2 units above and below the origion.
The student said the equation is (x^2/4)+(y^2/9)=1 ;however this is wrong because a^2 = 3^2= 9 because the vericies are three units away from the origin. Also, b^2 = 2^2 =4 , because the co-verticies are two units away from the origion.
The correct equation for the ellipse should be (x^2/9)+(y^2/4).

7:06 PM
Anonymous said...

The student wrote an equation for an ellipse with a vertical major axis but this ellipse has a horizontal major axis so a and b should be switched and the equation should be (x^2/9)+(y^2/4)=1

7:09 PM
Anonymous said...

the student did teh equation wrong. the graph is of a horizontal ellipse but the student made the equation if a verticle ellipse. i know this because the a (which is the larger variable) is under teh y^2. the equation shoudl be (x^2/9)+ (y^2/4)=1

10:29 PM
Anonymous said...

Error Analysis: x^2/4 + y^2/9 = 1, co-vertices (0, +/-2) vertices (+/-3,0)

The error is that the student did not input the correct values for a^2 and b^2 into the standard formula for an elipse with vertices on the x-axis, x^2/a^2 + y^2/b^2 = 1. In this case, a = +/-3, and b = +/-2. So, the correct equation should be x^2/9 + y^2/4 = 1.

12:03 AM
Anonymous said...

The student drew the ellipse horizontally where as it should be vertical because the y-value is 'a' and the vertexes should go vertically. 'a' is (0,3)(0,-3) 3 units over the origin and 3 units under the origin and 'b' is (2,0)(-2,0) 2 units to the right and left of the origin. The equation for the drawn ellipse is x^2/9+y^2/4=1

3:38 PM
Anonymous said...

The student switched a and b. If the equation was as the student wrote it, then the ellipse in the graph would be verticle, not horizontal. The correct equation of the shown ellipse is [(x^2)/9] + [(y^2)/4]

10:57 PM

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