Question

Question 14 Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0),

Class X1 - Maths -Conic Sections Page 262

Answer 1

A/C to question,
vertices ( ±7, 0) and e = 4/3
here,we can observe that vertices of hyperbola lies on X - axis. Let standard equation of hyperbola is x²/a² - y²/b² = 1

concept : - if vertices ( ±a, 0) of a hyperbola x²/a² - y²/b²= 1 then, c = ae and c² = a² + b²

now,
vertices ( ±7, 0) = ( ±a, 0)
hence, a = 7
c = 7 × 4/3 = 28/3

now, c² = a² + b²
b² = c² - a²
= (28/3)² - (7)²
= 784/9 - 49
= 343/9
b² = 343/9

hence, equation of hyperbola is
x²/49 - y²/(343/9) = 1
x²/49 - 9y²/343 = 1