AP EAMCET · Maths · Straight Lines
The origin is shifted to the point \((2,3)\) by translation of axes and then the coordinate axes are rotated about the origin through an angle \(\theta\) in the counter-clockwise sense. Due to this 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 \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(3 x^2+2 x y+3 y^2-18 x-22 y+50=0\) Shifting origin to the point \((2,3)\), put \(x=X+2, y=Y+3\) \(\begin{aligned} & 3(X+2)^2+2(X+2)(Y+3)+3(Y+3)^2 \\ & \quad-18(X+2)-22(Y+3)+50=0 \\ & \Rightarrow 3 X^2+2 X Y+3 Y^2-1=0 \end{aligned}\) Now, for rotating about \(\theta\) angle,…
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