Question

which of the following is the equation of a hyperbola with center at (0, 0), with $a = 4$, $b = 1$, opening horizontally?
$\frac{x^{2}}{1}-\frac{y^{2}}{16}=1$
$\frac{x^{2}}{16}-\frac{y^{2}}{1}=1$
$\frac{y^{2}}{16}-\frac{x^{2}}{1}=1$

Explanation:

Step1: Recall horizontal hyperbola formula

The standard equation for a horizontal hyperbola centered at $(0,0)$ is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.

Step2: Substitute given $a=4, b=1$

Calculate $a^2 = 4^2 = 16$ and $b^2 = 1^2 = 1$. Substitute into the formula: $\frac{x^2}{16} - \frac{y^2}{1} = 1$.

Step3: Match with options

Compare the derived equation to the provided choices.

Answer:

$\boldsymbol{\frac{x^2}{16}-\frac{y^2}{1}=1}$ (the second option)