Question
Question: The foci of a hyperbola coincide with the foci of the ellipse x<sup>2</sup>/25 + y<sup>2</sup>/9 = 1...
The foci of a hyperbola coincide with the foci of the ellipse x2/25 + y2/9 = 1. The equation of the hyperbola if its eccentricity is 2, is
A
x2/4 – y2/12 = 1
B
x2/12 – y2/4 = 1
C
x2/12 – y2/16 = 1
D
None of these
Answer
x2/4 – y2/12 = 1
Explanation
Solution
Foci of ellipse x2/25 + y2/9 = 1
are (± 4, 0) so foci of hyperbola are also (± 4, 0)
Ž ae = 4 Ž a × 2 = 4 Ž a = 2 …(i)
b2 = a2 (e2 – 1) = 4(4 – 1) Ž b2 = 12 ….(ii)
Equation x2/a2 – y2/b2 = 1 Ž x2/4 – y2/12 = 1