Question

Find the eccentricity and the coordinates of foci of the hyperbola 25x² + 9y² = 225.

Answer 1

25x² - 9y² = 225

The given equation can be written as

`(x^2)/(9) – (y^2)/(25)` = 1

Here, a² = 9 ⇒ a = 3 and b² = 25 ⇒ b = 5 

Eccentricity, 
e = `sqrt(1+(b^2)/(a^2))`

   = `sqrt(1+(25)/(9)`

   = `sqrt(34)/(9)`

   = `sqrt(34)/(3)`

Foci = (±ae,0)

   = `(±3 xx sqrt(34)/(3),0)`

   = `(±sqrt(34),0)`

Hence, the eccentricity and foci of the given hyperbola are `sqrt(34)/(3) "and" (±sqrt(34), 0)` respectively.