COMEDK · Maths · 15. Hyperbola
The distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt{2}\). Then its equation is
- A \(x^2-y^2=32\)
- B \(\dfrac{x^2}{4}-\dfrac{y^2}{9}=1\)
- C \(3 x^2-2 y^2=7\)
- D \(2 x^2-3 y^2=7\)
Answer & Solution
Correct Answer
(A) \(x^2-y^2=32\)
Step-by-step Solution
Detailed explanation
The distance between the foci of a hyperbola is given by \(2ae = 16\). Given the eccentricity \(e = \sqrt{2}\), we have \(2a\sqrt{2} = 16\), which simplifies to \(a\sqrt{2} = 8\), so \(a = \dfrac{8}{\sqrt{2}} = 4\sqrt{2}\). Squaring \(a\), we get…
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