Question

The equation of a hyperbola is $9x^{2}-16y^{2}=144$. If $A$ and $S$ are, respectively, the focus and the vertex of one section of the hyperbola, then the length of $AS$ is

• A. $\frac{5}{2}$
• B. $\frac{3}{2}$
• C. $\frac{1}{2}$
• D. 2
• E. 1

Hint:

Logic Tip: For the standard hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the distance from center to focus is $c$, where $c^2 = a^2 + b^2$. Here, $c^2 = 16 + 9 = 25 \implies c=5$. The vertex is at $a=4$. The distance between them is simply $c - a = 5 - 4 = 1$.

Answer 1

Answer: (E)