TS EAMCET · Maths · Pair of Lines
If \((h, k)\) is the new origin to be chosen to eliminate first degree terms from the equation \(\mathrm{S} \equiv 2 x^2-x y-y^2-3 x+3 y=0\) by translation and if \(\theta\) is the angle with which the axes are to be rotated about the origin in anticlockwise direction to eliminate xy-term from \(\mathrm{S}=0\), then \(\tan 2 \theta=\)
- A \(h+k\)
- B \(h-k\)
- C \(h k\)
- D \(-\frac{h}{3 k}\)
Answer & Solution
Correct Answer
(D) \(-\frac{h}{3 k}\)
Step-by-step Solution
Detailed explanation
\(h\), \(k\) are found by setting partial derivatives to zero: \(\frac{\partial S}{\partial x} = 4x - y - 3 = 0 \implies 4h - k = 3\) \(\frac{\partial S}{\partial y} = -x - 2y + 3 = 0 \implies -h - 2k = -3\)…
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