Question

Question 7 Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Class X1 - Maths -Conic Sections Page 262

Answer 1

concept : if ( 0, ± a) are vertices of hyperbola.
then equation of hyperbola will be of the form
x²/a² - y²/b² = 1 . and foci of hyperbola will be ( ± c, 0) where c² = a² + b².

A/C to question,
vertices ( ±2 , 0) = (± a , 0)
hence, a = 2 ________(1)

Foci ( ±3, 0) = ( ± c , 0)
hence, c = 3 _________(2)

now, use, c² = a² + b² by using equations (1) and (2) . we get ,
3² = 2² + b²
9 = 4 + b² => b² = 5 _________(3)

now, equation of hyperbola :
x²/a² - y²/b² = 1
x²/(2)² - y²/5 = 1 [ by putting values of a and b² from equations (2) and (3) ]
Hence,
${ \frac{ {x}^{2} }{4} - \frac{ {y}^{2} }{5} = 1}$