AP EAMCET · Maths · Straight Lines
The angle through which the coordinate axes are to be rotated to remove the \(x y\) term in the equation \(x^2+2 x y-y^2=0\) is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{8}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{8}\)
Step-by-step Solution
Detailed explanation
Given equation is \(x^2+2xy-y^2=0\), so \(A=1\), \(B=2\), \(C=-1\). \(\tan(2\theta) = \frac{B}{A-C}\) \(\tan(2\theta) = \frac{2}{1 - (-1)}\) \(\tan(2\theta) = \frac{2}{2} = 1\) \(2\theta = \frac{\pi}{4}\) \(\theta = \frac{\pi}{8}\)
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