Answer:
center: (0,0)
vertices: (-4,0) and (4,0)
foci: (-10.8,0) and (10.8,0)
asymptotes: y = -5/2*x and y = 5/2*x
Explanation:
Hyperbola with center as origin general equation is:
x²/a² - y²/b² = 1
Our equation is:
25x² - 4y² = 400
Dividing each term by 400:
25x²/400 - 4y²/400 = 400/400
x²/16 - y²/100 = 1
which matches the general equation. Then, the center is (0,0)
a² = 16
a = 4
b² = 100
b = 10
c² = a² + b²
c = √(16+100) = 10.8
General vertices formula: (±a,0). Replacing, the vertices are: (-4,0) and (4,0)
General foci formula: (±c,0). Replacing, the foci are: (-10.8,0) and (10.8,0)
General asymptotes formula: y = ±b/a*x. Replacing, the asymptotes are:
y = -10/4*x = -5/2*x
y = 10/4*x = 5/2*x