1. a) Transform to co-ordinates of the equations (i) $r(cos2\theta + sin2\theta) = 5k sin\theta cos\theta$ (ii) $x^3 = y^2(2a - x)$ b) Find the transformed equation of $x^2 + 2\sqrt{3}xy - y^2 = 2a^2$, when the axes are rotated through an angle $\frac{\pi}{6}$
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To find the transformed coordinates, we need to rotate the axes through an angle. Let's call this angle θ. The transformation equations for rotating the axes are: x' = x*cosθ - y*sinθ y' = x*sinθ + y*cosθ Substituting these equations into the given equation, we Show more…
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