AP EAMCET · Maths · Straight Lines
If the origin is shifted to \((2,3)\) and the axes are rotated through an angle \(45^{\circ}\) about that point, then the transformed equation of \(2 x^2+2 y^2-8 x-12 y+18=0\) is
- A \(x^2-7 y^2-14 x y-2=0\)
- B \(x^2+y^2=4\)
- C \(x^2-y^2=4\)
- D \(8 x^2-2 y^2=9\)
Answer & Solution
Correct Answer
(B) \(x^2+y^2=4\)
Step-by-step Solution
Detailed explanation
Given, equation is \[ \begin{array}{rlrl} & & 2 x^2+2 y^2-8 x-12 y+18 & =0 \\ \Rightarrow & 2(x-2)^2+2(y-3)^2 & =8 \\ \Rightarrow & (x-2)^2+(y-3)^2 & =4 \end{array} \] After the shifting of origin to \((2,3)\), the transformed equation becomes \(x^2+y^2=4\) and after the…
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