Determining restrictions on an ellipse

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In summary, if A and B are both greater than 0, the equation Ax^2 + By^2 + Cx = 1 represents an ellipse. To have the major axis of the ellipse on the y-axis, the condition must be C = 0 and A > B. This was initially thought to be A < B, but testing with a plotted ellipse confirms that A > B is the correct condition. If B > A, the major axis will run along the y-axis. Additionally, if C is not equal to 0, the center of the ellipse will be shifted from the center of coordinates.
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trigger352
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The equation [tex]Ax^2 + By^2 + Cx = 1 [/tex] represents an ellipse. If [tex]A > 0[/tex] and [tex]B > 0[/tex], what conditions must be satisfied if the ellipse has it's major axis on the y-axis?

The answer is "[tex] C = 0[/tex] and [tex]A > B[/tex]"

When I first wrote this question I thought [tex]A > B[/tex] should have been [tex]A < B[/tex]. So how do I figure out what the restrictions are? Why is [tex]A < B[/tex] wrong?
 
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Plot an ellipse where A > B and see if the answer is correct... then test your way of A < B.

Jameson

BTW: Your answer is correct. If B > A , then the major axis will run along the y-axis.
 
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C different from zero would automatically shift the center of the ellipse from the center of coordinates...

Daniel.
 

FAQ: Determining restrictions on an ellipse

What is an ellipse and how is it defined?

An ellipse is a geometric shape that resembles a flattened circle. It is defined as a set of points in a plane, such that the sum of the distances from any point on the ellipse to two fixed points (called the foci) is constant.

What are the restrictions on an ellipse?

The main restriction on an ellipse is that it must have a major axis and a minor axis, which are perpendicular to each other and intersect at the center of the ellipse. Additionally, the length of the major axis must be greater than or equal to the length of the minor axis.

How do you determine the equation of an ellipse?

The standard form of the equation of an ellipse is (x-h)^2/a^2 + (y-k)^2/b^2 = 1, where (h,k) is the center of the ellipse and a and b are the lengths of the major and minor axes, respectively.

What is the significance of the eccentricity of an ellipse?

The eccentricity of an ellipse is a measure of how stretched out or elongated the ellipse is. It is defined as the ratio of the distance between the foci to the length of the major axis. An eccentricity of 0 indicates a circle, while an eccentricity of 1 indicates a line segment.

How do you determine the restrictions on an ellipse from its equation?

By examining the coefficients in the standard form of the equation (x-h)^2/a^2 + (y-k)^2/b^2 = 1, we can determine the center of the ellipse (h,k) and the lengths of the major and minor axes (a and b). We can also calculate the eccentricity and determine if the ellipse is a circle, an elongated ellipse, or a line segment.

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