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If the axes are rotated through an angle 30° then the coordinates of (0, 5) in the new system $(\frac{a}{2}, \frac{b}{2})$

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$b = - 2 \sqrt{3}$

$b = 5 \sqrt{3}$

a=5

$b = - 5 \sqrt{3}$

answer is A, C.

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Detailed Solution

$\begin{aligned} X = x \cos θ + y \sin θ \\ Y = - x \sin θ + y \cos θ \end{aligned} \Rightarrow \frac{a}{2} = \frac{5}{2}, \frac{b}{2} = \frac{5 \sqrt{3}}{2} \Rightarrow a = 5, b = 5 \sqrt{3}$

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