AP EAMCET · Maths · Straight Lines
Find the transformed equation of the curve \(x^2+2 \sqrt{3} x y-y^2=8\), when the axes are rotated through an angle \(\frac{\pi}{3}\).
- A \(x^2+y^2+2 \sqrt{3} x y=8\)
- B \(x^2+y^2-2 \sqrt{3} x y=8\)
- C \(x^2-y^2+2 \sqrt{3} x y=8\)
- D \(x^2-y^2-2 \sqrt{3} x y=8\)
Answer & Solution
Correct Answer
(D) \(x^2-y^2-2 \sqrt{3} x y=8\)
Step-by-step Solution
Detailed explanation
Given equation, \(x^2+2 \sqrt{3} x y-y^2=8\) Since, the axes are rotated through an angle \(\pi / 3\). \(\therefore(x, y)\) replaced by \(\left(x \cos \frac{\pi}{3}-y \sin \frac{\pi}{3}, x \sin \frac{\pi}{3}+y \cos \frac{\pi}{3}\right)\) i.e.…
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