Question

3. When the axes are rotated through an angle o, find the transformed equation of
x cosa – vaid = p.​

Answer 1

Answer:

Let (X, Y) be the new coordinates of (x, y)

So, x = X cosα – Y sinα, y = X sinα + Y cosα

The transformed equation is (X cosα – Y sinα) cosα + (X sinα + Y cosα) sinα = p

=> X cos2α – Y sinα cosα + Y sin2α + Y cosα sinα = p

=> X(cos2α + sin2α) = p

=>X = p.

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