AP 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 :
- A \(15 x^2-14 x y+3 y^2=20\)
- B \(15 x^2+14 x y-3 y^2=20\)
- C \(15 x^2+14 x y+3 y^2=20\)
- D \(15 x^2-14 x y-3 y^2=20\)
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…
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