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TS EAMCET · Maths · Pair of Lines

The transformed equation of \(x^2+6 x y+8 y^2=10\) when the axes are rotated through an angle \(\frac{\pi}{4}\) is :

  1. A \(15 x^2-14 x y+3 y^2=20\)
  2. B \(15 x^2+14 x y-3 y^2=20\)
  3. C \(15 x^2+14 x y+3 y^2=20\)
  4. D \(15 x^2-14 x y-3 y^2=20\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(15 x^2+14 x y+3 y^2=20\)

Step-by-step Solution

Detailed explanation

The given equation is \(x^2+6 x y+8 y^2=10\) \(\ldots\) (i) Since axes are rotated through an angle \(\frac{\pi}{4}\). \(\therefore \quad x=x_1 \cos \frac{\pi}{4}-y_1 \sin \frac{\pi}{4}=\frac{x_1-y_1}{\sqrt{2}}\) and…