TS EAMCET · Maths · Straight Lines
When the origin is shifted to the point \(\mathrm{P}\) by translation of axes, the equation \(2 x^2+y^2-4 x+4 y=0\) is transformed to \(2 x^2+y^2-8 x+8 y+18=0\). Then the transformed equation of the straight line \(x+2 y+2=0\) if the origin is shifted to the same point \(\mathrm{P}\) is
- A \(x+2 y-1=0\)
- B \(x+2 y-3=0\)
- C \(x+2 y+7=0\)
- D \(x+2 y+5=0\)
Answer & Solution
Correct Answer
(D) \(x+2 y+5=0\)
Step-by-step Solution
Detailed explanation
Let origin is shifted to the point \(P(h, k)\) then put \(X=x+h\) and \(Y=y+k\), we get \(\begin{aligned} & 2(x+h)^2+(y+k)^2-4(x+h)+4(y+k)=0 \\ & \Rightarrow \quad 2 x^2+y^2+(4 h-4) x\end{aligned}\) \(+(2 k+4) y+2 h^2+k^2-4 h+4 k=0\) comparing with \(2 x^2+y^2-8 x+8 y+18=0\), we…
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