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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
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'
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
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?
30 degrees
45 degrees
60 degrees
Which angle of rotation will eliminate the x y term from the equation when rotating the axes for a parabola?
When rotating the axes for a parabola, the primary goal is to eliminate which term from the equation?
x
y
xy
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
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.
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, what aspect of the equation remains unchanged?
The vertex coordinates
the orientation of the parabola
The value of the constant p
It is done.