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Which of the following statements is true regarding the equation of a parabola after rotating the axes?
The equation always becomes linear
The equation remains the same
The equation can become simpler by eliminating cross-terms
Which angle of rotation will eliminate the x y term from the equation when rotating the axes for a parabola?
30 degrees
45 degrees
60 degrees
For a parabola in standard form x2=4py, what is the equation of the rotated parabola after rotating the axes by 30 degrees?
y′2=8 px'
y′2=2 px'
y′2=4 px'
For a parabola in standard form y2= 4px, if the rotation angle θ is such that cos(2θ) =0, what is the value of θ?
θ=0
θ=π/4
θ=π/2
When rotating the axes for a parabola, the primary goal is to eliminate which term from the equation?
x
y
xy
What is the effect of rotating the axes for a parabola on its vertex?
The vertex shifts along the major axis.
The vertex shifts along the minor axis.
The vertex remains unchanged.
When rotating the axes for a parabola, what aspect of the equation remains unchanged?
The vertex coordinates
the orientation of the parabola
The value of the constant p
If the equation of a parabola is y2 =8x, what is the equation of the rotated parabola after rotating the axes by 45 degrees?
y′2= x'
y2=8x
None
If a parabola opens to the left, what angle of rotation should be used to align its major axis with one of the coordinate axes?
When rotating the axes for a hyperbola, what aspect of the equation remains unchanged?
The orientation of the transverse axis
The value of the constant c
The distance between the vertices
It is done.