TS EAMCET · Maths · Straight Lines
By shifting the origin to the point \((2,3)\) and then rotating the coordinate axes through an angle \(\theta\) in the counter clockwise direction, if the equation \(3 x^2+2 x y+3 y^2-18 x-22 y+50=0\) is transformed to \(4 X^2+2 Y^2-1=0\), then the angle \(\theta=\)
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
By shifting the origin to the point \((2,3)\) and then rotating the coordinate axes through an angle \(\theta\) in counter clockwise direction, the \(x=2+X \cos \theta-Y \sin \theta\) and \(y=3+x \sin \theta+y \cos \theta\), so the given equation…
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