Ox5 foci Solutionits a horizontal hyperbola xh2a2 yk2b2 1

Solution

its a horizontal hyperbola

(x-h)²/a² - (y-k)²/b² = 1

as both the foci are on x-axis and are symmetric about y-axis => h = 0 and k = 0

so center is (0,0)

now c = distance between center and foci = sqrt(7)

also slope of asymptotes = b/a = sqrt(10)/5

==> b² = (10/25)a² = 0.4a²

also c² = a² + b² ==> 7 = a² + 0.4a² ==> a² = 5

====> b² = 2

====> equation of hyperbola, x²/5 - y²/2 = 1