TS EAMCET · Maths · Pair of Lines
When the origin is shifted to the point \((h, k)\) by translati:g the coordinate axes, the equation \(S=2 x^2-x y+y^2+2 x\) \(+3 y+1=0\) is changed to \(S^{\prime}=a x^2+2 h x y+b y^2-3\) \(=0\). Again by rotating the coordinate axes about the new origin through the angle \(\theta\) in the positive direction, \(\mathrm{S}^{\prime}=0\) is changed to \(\mathrm{Ax}^2+\mathrm{By}^2+\mathrm{C}=0\). Then \(\mathrm{h}+\mathrm{k}+\tan 2 \theta=\)
- A -4
- B 0
- C 1
- D none of these
Answer & Solution
Correct Answer
(D) none of these
Step-by-step Solution
Detailed explanation
When origin is shifted to \((h, k)\), let new \(x\) and \(y\) co-ordinates \((X, Y)\) in place of \((x, y)\). \[ \begin{aligned} & X=x-h \\ & Y=y-k \end{aligned} \] In this question, any one of \(\mathrm{S}\) or \(\mathrm{S}^1\) contains some error.
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