Question

identify the graph of $\frac{x^{2}}{4}-\frac{y^{2}}{36}=1$.

Explanation:

Step1: Identify the conic - section type

The equation $\frac{x^{2}}{4}-\frac{y^{2}}{36}=1$ is of the form $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}} = 1$, which represents a hyperbola with a horizontal transverse axis.

Step2: Recall the characteristics of a hyperbola

For a hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$, the vertices are at $(\pm a,0)$. Here $a^{2}=4$, so $a = 2$ and the vertices are at $(\pm2,0)$.

Answer:

A. Option Text