Question

identify this conic section. $x^2 - y^2 = 16$
circle
parabola
hyperbola
ellipse
line

Explanation:

Step1: Recall conic standard forms

The general form of a hyperbola with transverse axis along the x-axis is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.

Step2: Rewrite given equation

Divide both sides by 16 to match the standard form:
$\frac{x^2}{16} - \frac{y^2}{16} = 1$
This fits the hyperbola form where $a^2=16$ and $b^2=16$.

Answer:

hyperbola