AP EAMCET · Maths · Straight Lines
When the origin is shifted to the point \((2,3)\) and then the coordinate axes are rotated through an angle \(\frac{\pi}{3}\) in the counter clockwise sense, then the transformed equation of \(3 x^2+2 x y+3 y^2-18 x-22 y+50=0\) is
- A \(3 x^2+3 y^2-1=0\)
- B \((6+\sqrt{3}) x^2-2 x y+(6-\sqrt{3}) y^2-2=0\)
- C \(4 x^2+2 y^2-1=0\)
- D \((6-\sqrt{3}) x^2+(6+\sqrt{3}) y^2+2 x y=0\)
Answer & Solution
Correct Answer
(B) \((6+\sqrt{3}) x^2-2 x y+(6-\sqrt{3}) y^2-2=0\)
Step-by-step Solution
Detailed explanation
We first change the origin, by putting \(x^{\prime}+2\) and \(y^{\prime}+2\) for \(x\) and \(y\) respectively. The new equation will be…
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