AP EAMCET · Maths · Pair of Lines
By rotating the axes about the origin in anti-clockwise direction with certain angle, if the equation \(\mathrm{x}^2+4 \mathrm{xy}+\mathrm{y}^2=1\) is transformed to \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) then \(\sqrt{\frac{a^2+b^2}{a^2}}=\)
- A 2
- B \(\frac{\sqrt{13}}{3}\)
- C \(\frac{3}{2}\)
- D \(\sqrt{10}\)
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\(M = \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}\) \(\det(M - \lambda I) = (1-\lambda)^2 - 4 = 0\) \(1-\lambda = \pm 2 \implies \lambda_1 = 3, \lambda_2 = -1\) \(3x'^2 - y'^2 = 1 \implies \frac{x'^2}{1/3} - \frac{y'^2}{1} = 1\) \(a^2 = 1/3, b^2 = 1\)…
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