Find the transformed equation of x cos ⁡ +y sin ⁡ =p, when the axes are rotated through an angle .

Question

Accepted Answer

Correct answer: A. (a) Given equation is r cos ⁡ +y sin ⁡ =P The axis are rotated through angle ( ), then x=X cos ⁡ -Y sin ⁡ and y=X sin ⁡ +Y sin ⁡ Put in Eq. (i) cos ⁡ (X cos ⁡ -Y sin ⁡ )+ sin ⁡ (X sin ⁡ +Y cos ⁡ ) ⇒X cos^2 ⁡ -Y sin ⁡ cos ⁡ +X sin^2 ⁡ +Y sin ⁡ cos ⁡ =P ⇒X=P

$Find the transformed equation of x cos θ + y sin θ = p, when the axes are rotated through an angle θ .$

Solution

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