If the axes are rotated through 60° in the anti-clockwise sense. find the transformed form of the equation x2 - y2 = a?
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Step-by-step explanation:
when the axes are rotated through an angle alpha, find the transformed equation of xcosalpha +ysin alpha=p
xcosα + ySinα = p
The axes are rotated through an angle α
x = X Cosα - Y Sinα
y = Xsinα + YCosα
putting these values
(X Cosα - Y Sinα)cosα + (Xsinα + YCosα)Sinα = p
=> XCos²α - YSinαcosα + XSin²α + YCosαSinα = p
=> X(Cos²α + Sin²α) = p
=> X = p
Transformed equation is X = p
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