AP EAMCET · Maths · Straight Lines
When the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the positive direction, an equation is transformed to \(x^2+y^2-6 x+8 y+21=0\). Then that original equation is
- A \(x^2+y^2-7 \sqrt{2} x+\sqrt{2} y+21=0\)
- B \(\sqrt{2} x^2+\sqrt{2} y^2-7 x+y+21 \sqrt{2}=0\)
- C \(x^2+y^2-14 x+2 y+21=0\)
- D \(x^2+y^2-7 \sqrt{2} x+\sqrt{2} y+21 \sqrt{2}=0\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2-7 \sqrt{2} x+\sqrt{2} y+21=0\)
Step-by-step Solution
Detailed explanation
\( x' = x \cos\left(\frac{\pi}{4}\right) + y \sin\left(\frac{\pi}{4}\right) = \frac{x+y}{\sqrt{2}} \) \( y' = -x \sin\left(\frac{\pi}{4}\right) + y \cos\left(\frac{\pi}{4}\right) = \frac{-x+y}{\sqrt{2}} \)…
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