COMEDK · Maths · 15. Hyperbola
The difference between the distance of any point on the hyperbola from the two foci is 16 and the eccentricity is 2. Then the equation of the hyperbola is
- A \(\dfrac{x^2}{64} - \dfrac{y^2}{192} = 1\)
- B \(\dfrac{x^2}{64} - \dfrac{y^2}{256} = 1\)
- C \(\dfrac{x^2}{64} - \dfrac{y^2}{64} = 1\)
- D \(\dfrac{x^2}{192} - \dfrac{y^2}{64} = 1\)
Answer & Solution
Correct Answer
(A) \(\dfrac{x^2}{64} - \dfrac{y^2}{192} = 1\)
Step-by-step Solution
Detailed explanation
The difference between the distances of any point on a hyperbola from its two foci is equal to the length of the transverse axis, which is \(2a\). Given \(2a = 16\), which gives \(a = 8\). The eccentricity is given as \(e = 2\). For a hyperbola, the relation between \(a\),…
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