NDA Math Trigonometric Ratios of Angles and Equations

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Consider the following for the next 03 (three) items:
If p = X cos θ−Y sin θ , q = X sin θ + Y cos θ and p 2 + 4pq + q 2 = A X 2 + BY 2 , 0≤ θ ≤
π
2
[NDA I 2019]
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