Given, Hyperbola equation: 25x2−75y2=225 Divide both sides by 225 to obtain standard form:
25x2
225
−
75y2
225
=1⟹
x2
9
−
y2
3
=1 Thus, a2=9 and b2=3. Compute c from c2=a2+b2 : c2=9+3=12⇒c=√12=2√3 The foci are at (±c,0), so the distance between them is 2 c : 2c=2×2√3=4√3 ∴ The distance between the two foci is 4√3 units.