Question

The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:

• A. 10
• B. 5
• C. 20
• D. 40

Hint:

For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the distance between the foci is \( 2c \), where $c^2 = a^2 + b^2$.

Answer 1

The Correct Option is A

Step 1: Identify \( a^2 \) and \( b^2 \).
For the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \), $a^2 = 16$ and $b^2 = 9$. Step 2: Calculate \( c \).
$c^2 = a^2 + b^2 = 16 + 9 = 25 \implies c = 5$. Step 3: Determine the distance between the foci.
The foci are at \( (\pm c, 0) \), which are \( (5, 0) \) and \( (-5, 0) \). The distance between them is $2c = 2 \times 5 = 10$.