AP EAMCET · Maths · Straight Lines
If the origin is shifted to the point \((1,1)\) and the axes are rotated through an angle \(45^{\circ}\) about this point, then the transformed equation of the equation \(x^2+2 x y+y^2-1=0\) is
- A \(2 y^2-4 \sqrt{2} y-3=0\)
- B \(2 y^2+4 \sqrt{2} y-3=0\)
- C \(2 x^2+4 \sqrt{2} x+3=0\)
- D \(2 x^2-4 \sqrt{2} x+3=0\)
Answer & Solution
Correct Answer
(C) \(2 x^2+4 \sqrt{2} x+3=0\)
Step-by-step Solution
Detailed explanation
\((x+y)^2-1=0\) \(x=x'+1, y=y'+1 \implies (x'+1+y'+1)^2-1=0 \implies (x'+y'+2)^2-1=0\) \(x' = \frac{X-Y}{\sqrt{2}}, y' = \frac{X+Y}{\sqrt{2}} \implies x'+y' = \sqrt{2}X\) \((\sqrt{2}X+2)^2-1=0\) \(2X^2+4\sqrt{2}X+4-1=0\) \(2X^2+4\sqrt{2}X+3=0\)
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