In the same hyperbola, what is c if the foci are at (±c, 0)?

In the same hyperbola, what is c if the foci are at (±c, 0)?

• A. 5
• B. 3
• C. √34
• D. √50

Answer: (C)

For a hyperbola with a horizontal transverse axis, the foci are at (±c, 0) and the relationship c^2 = a^2 + b^2 holds. That means c is the square root of the sum of the squares of the semi-axes. In this hyperbola, a^2 and b^2 add up to 34, so c^2 = 34, giving c = sqrt(34). The other numerical choices would correspond to different sums a^2 + b^2.

For a hyperbola with a horizontal transverse axis, the foci are at (±c, 0) and the relationship c^2 = a^2 + b^2 holds. That means c is the square root of the sum of the squares of the semi-axes.

In this hyperbola, a^2 and b^2 add up to 34, so c^2 = 34, giving c = sqrt(34). The other numerical choices would correspond to different sums a^2 + b^2.