WBJEE · Maths · Hyperbola
The average length of all vertical chords of the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1, a \leq x \leq 2 a\), is
- A \(\mathrm{b}\{2 \sqrt{3}+\ell n (2+\sqrt{3})\}\)
- B \(b\{3 \sqrt{2}+\ell \ln (3+\sqrt{2})\}\)
- C \(\mathrm{a}\{2 \sqrt{5}-\ell \mathrm{n}(2+\sqrt{5})\}\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
Hint : \(A_L=\frac{2 \int_a^{2 a} y d x}{\int_a^{2 a} d x}\) \(=\frac{2 \int_a^{2 a} \frac{b}{a} \sqrt{x^2-a^2} d x}{\int_a^{2 a} d x}=b[2 \sqrt{3}-\ell \mathrm{n}(2+\sqrt{3})]\)
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