TS EAMCET · Maths · Hyperbola
If \(p, q\) are the eccentricities of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate hyperbola respectively, then the area of the square (in sq. units) formed by the points of intersection of the ellipse \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1\) and the pair of lines \(x^2-y^2=0\) is
- A 4
- B \(\sqrt{2}\)
- C \(\frac{\sqrt{3}}{2}\)
- D 16
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(p\) and \(q\) are eccentricity of hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) and its conjugate of hyperbola, \(\therefore \quad p^2=\frac{a^2+b^2}{a^2} \text { and } q^2=\frac{a^2+b^2}{b^2}\) \(\frac{x^2}{p^2}+\frac{y^2}{q^2}=1 \Rightarrow a^2 x^2+b^2 y^2=a^2+b^2\) ...(i)…
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