AP EAMCET · Maths · Pair of Lines
Suppose the axes are to be rotated through an angle \(\theta\) so as to remove the \(x y\) form from the equation \(3 x^2+2 \sqrt{3} x y\) \(+y^2=0\). Then in the new coordinate system the equation \(x^2+y^2+2 x y=2\) is transformed to
- A \((2+\sqrt{3}) x^2+(2-\sqrt{3}) y^2+2 x y=4\)
- B \((2+\sqrt{3}) x^2+(2+\sqrt{3}) y^2-2 x y=4\)
- C \(x^2+y^2-2(2-\sqrt{3}) x y=4(2-\sqrt{3})\)
- D \(x^2+y^2+2(2+\sqrt{3}) x y=4(2+\sqrt{3})\)
Answer & Solution
Correct Answer
(A) \((2+\sqrt{3}) x^2+(2-\sqrt{3}) y^2+2 x y=4\)
Step-by-step Solution
Detailed explanation
Let axes be rotated through an angle \(\theta\), then old coordinates are \(\begin{aligned} & x=X \cos \theta-Y \sin \theta \\ & y=X \sin \theta+Y \cos \theta \end{aligned}\) Putting given equation \(3 x^2+2 \sqrt{3} x y+y^2=0\)…
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