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March 12th, 2014, 11:59 PM   #1
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Translation and Rotation of Axes Problem

The equation of a parabola in the x''y'' plane is (y'')^2=4x''. The equation of that parabola in the x'y' plane is (y'-3)^2 = 4(x'-6). How do I get the original equation of that parabola in the xy plane before the axes rotated? (The x'y' plane was rotated to an angle of 45 degrees).

Please help. This is confusing.

I know that x = (x')costheta - (y')sintheta and y = (x')sintheta + (y')costheta and that's all I know

The graph looks something like this:
http://tinypic.com/r/332s1uv/8
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March 13th, 2014, 01:04 AM   #2
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Re: Translation and rotation of axes

Rewrite and in terms of and and substitute into the second equation. The equation in will be that of the curve in the plane.

By the way the first equation shows that the plane is a translation of the plane. Did you notice it?
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March 14th, 2014, 03:56 AM   #3
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Re: Translation and Rotation of Axes Problem

So I just have to use the formula x' = xcostheta + ysintheta and y' = -xsintheta + ycostheta and plug them into (y'-3)^2 = 4(x'-6), then simplify the equation and that's the equation in the xy plane? Am I right?
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