AP EAMCET · Maths · Pair of Lines
The transformed equation of \(3 x^2-4 x y=r^2\) when the coordinate axes are rotated about the origin through an angle of \(\operatorname{Tan}^{-1}(2)\) in positive direction is
- A \(x^2-4 y^2=r^2\)
- B \(2 x y+r^2=0\)
- C \(4 y^2-x^2=r^2\)
- D \(x y=r^2\)
Answer & Solution
Correct Answer
(C) \(4 y^2-x^2=r^2\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Tan}^{-1}(2) \implies \tan\theta = 2\) \(\sin\theta = \frac{2}{\sqrt{5}}, \cos\theta = \frac{1}{\sqrt{5}}\) \(x = x'\cos\theta - y'\sin\theta = \frac{1}{\sqrt{5}}(x' - 2y')\) \(y = x'\sin\theta + y'\cos\theta = \frac{1}{\sqrt{5}}(2x' + y')\)…
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