Graphing an Equation Using Rotation of Axes. Show that the graph of the equation
is part of a parabola by rotating the axes though an angle of . [Hint: First convert the equation to one that does not involve radicals.]
The equation represents a parabola by rotating the axes.
The given equation is,
Rotate the axes by an angle of .
The standard equation of a conic is,
Suppose the and axes in a coordinate plane are rotated through the acute angle to produce the and axes. Then, the coordinates and of a point in the and planes are related as,
First, remove the radicals from the given equations,
Equation represents the given equation after radicals are removed.
The axes have to be rotated by an angle of .
Substitute for in equations and to get,
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