TS EAMCET · Maths · Straight Lines
Suppose the new axes \(X, Y\) are generated by rotating the coordinate axes \(x, y\) about the origin through an angle of \(30^{\circ}\) in the anti-clockmise direction. Then, the transformed equation of \(x^2+2 \sqrt{3} x y-y^2=2 a^2\) with respect to new axes \(X, Y\) is
- A \(X^2-Y^2=a^2\)
- B \(X^2+Y^2=2 a^2\)
- C \(X^2+2 \sqrt{3} X Y-Y^2=2 a^2\)
- D \(X^2-Y^2=2 a^2\)
Answer & Solution
Correct Answer
(A) \(X^2-Y^2=a^2\)
Step-by-step Solution
Detailed explanation
The given equation is \[ x^2+2 \sqrt{3} x y-y^2=2 a^2 \] Since, axes are rotated through an angle \(30^{\circ}\).…
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