For the hyperbola x^2/25 - y^2/9 = 1, the foci lie at (±c, 0). Which of the following gives c?

For the hyperbola x^2/25 - y^2/9 = 1, the foci lie at (±c, 0). Which of the following gives c?

• A. 5
• B. √34
• C. √50
• D. 3

Answer: (B)

For a hyperbola in standard form x^2/a^2 - y^2/b^2 = 1, the foci are at (±c, 0) where c^2 = a^2 + b^2. Here a^2 = 25 and b^2 = 9, so c^2 = 25 + 9 = 34, giving c = sqrt(34). This value is the distance from the center to each focus, matching the (±c, 0) placement. The other numbers would correspond to a or b (or would imply a different sum a^2 + b^2), so they don’t fit as the focus distance.

For a hyperbola in standard form x^2/a^2 - y^2/b^2 = 1, the foci are at (±c, 0) where c^2 = a^2 + b^2. Here a^2 = 25 and b^2 = 9, so c^2 = 25 + 9 = 34, giving c = sqrt(34). This value is the distance from the center to each focus, matching the (±c, 0) placement. The other numbers would correspond to a or b (or would imply a different sum a^2 + b^2), so they don’t fit as the focus distance.