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When performing a rotation of axes for an ellipse, what is the main advantage?
It changes the center of the ellipse
It changes the size of the ellipse
It simplifies the equation of the ellipse and aligns it with the principal axes
During a rotation of axes for an ellipse, which term remains unchanged in the equation?
The squared terms involving x and y
the coefficients of the squared terms
The constant term
In the context of rotating axes for an ellipse, what angle should be chosen to align the new axes with the major and minor axes of the ellipse?
90 degrees
the angle that makes the major axis vertical
Any arbitrary angle
After performing a rotation of axes for an ellipse, what term might appear in the simplified equation that wasn't present in the original equation?
the term involving the original coordinates (x, y)
The term involving the new coordinates (x', y')
After performing a rotation of axes, the new equation for an ellipse has a term x y'. What does this term indicate?
What is the primary goal of performing a rotation of axes for an ellipse?
To change the shape of the ellipse
To increase the length of the major axis
To simplify the equation of the ellipse and align it with the coordinate axes
For an ellipse with a vertical major axis, what angle of rotation should be used to align the new axes with the major and minor axes of the ellipse?
0 degrees
45 degrees
When performing a rotation of axes for an ellipse, what happens to the lengths of the semi- major and semi-minor axes?
They both increase
They both decrease
The semi-major axis increases while the semi- minor axis decreases
If the original ellipse's major axis is horizontal, what angle of rotation should be chosen to align the new axes with the major and minor axes of the ellipse?
When rotating the axes for an ellipse, what is the purpose of adjusting the angle of rotation?
to increase the eccentricity of the ellipse
To align the new axes with the major and minor axes of the original ellipse
It is done.