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anonymous
 one year ago
How do you know when an ellipse is parallel to the xaxis or yaxis? For example, If I'm given 4x^216x+9y^2+18y11=0 and I simplify that into an equation of an ellipse: [(x2)^2]/[9] + [(y1)^2]/[4] = 1, how do I know if the ellipse is parallel to the xaxis or parallel to the yaxis?
anonymous
 one year ago
How do you know when an ellipse is parallel to the xaxis or yaxis? For example, If I'm given 4x^216x+9y^2+18y11=0 and I simplify that into an equation of an ellipse: [(x2)^2]/[9] + [(y1)^2]/[4] = 1, how do I know if the ellipse is parallel to the xaxis or parallel to the yaxis?

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Not exactly sure what you mean by "parallel." Maybe you mean whether the ellipse is wide along the xaxis or tall along the yaxis? :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1As in this vs. this?dw:1439526085570:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, Im trying to solve this problem: Find the center, vertices, and foci of the ellipse given by 4x^2  16x + 9y^2 + 18y  11 = 0 I have figured everything out till: [(x2)^2]/[9] + [(y1)^2]/[4] = 1 Now i have to find the foci and vertices, but there are two different expressions used to find the foci and vertices, and they both depend on whether your ellipse is parallel to the xaxis or yaxis...

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, I get what you mean. I had never heard that terminology before, but we are both thinking of the same thing. I believe you should have (y+1)^2/4 in your expression rather than (y1)^2/4, but aside from that... whichever expression has the larger denominator will be the major axis. Since your expression for x^2 has the larger denominator 9, the ellipse will be parallel to the xaxis.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1In fact, the denominators are the radius of the axis squared. So in this case, the major axis has a radius of 3 along the xaxis, since 3^2 = 9. The minor axis has a radius of 2 along the yaxis, since 2^2 = 4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439526368806:dw This is what I'm looking at..

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, openstudy didn't tell me that you had replied.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1OK, yes my explanation above still stands. It is the "major axis" that is parallel, not the "ellipse" that is parallel just for future terminology. Do you understand the table though?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Remember that the general equation of an ellipse is represented by \[\frac{(xh)^2}{first\ denominator^2} + \frac{(yk)^2}{second \ denominator^2} = 1\] and we make "a" the bigger of the two denominators, while "b" is the smaller of the two denominators according to your table. So, in your case, we have \[\frac{(xh)^2}{a^2} + \frac{(yk)^2}{b^2} = 1\] since the xdenominator was bigger.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1What you should have for your question is that a = 3 and b = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you very much, I worked the rest out and it matched the answer key. This is valuable information, I appreciate it! @jtvatsim

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.1Great job! I'm glad you figured it out! :)
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