Question

question 6 of 10
which formula represents the hyperbola on the graph shown below?
a. $\frac{(x - 3)^2}{169}-\frac{(y + 2)^2}{81}=1$
b. $\frac{(y - 3)^2}{169}-\frac{(x + 2)^2}{81}=1$
c. $\frac{(x + 3)^2}{81}-\frac{(y - 2)^2}{169}=1$
d. $\frac{(y + 3)^2}{169}-\frac{(x - 2)^2}{81}=1$

Explanation:

Step1: Identify the orientation of the hyperbola

The hyperbola opens left - right as it has branches extending horizontally. The standard form of a hyperbola opening left - right is $\frac{(x - h)^2}{a^2}-\frac{(y - k)^2}{b^2}=1$, where $(h,k)$ is the center of the hyperbola.

Step2: Analyze the center of the hyperbola

The center of the hyperbola is at the mid - point of the vertices. From the graph, the center is at $(3,-2)$.

Step3: Match the formula with the center and orientation

For a hyperbola with center $(h = 3,k=-2)$ and opening left - right, the formula is $\frac{(x - 3)^2}{a^2}-\frac{(y+2)^2}{b^2}=1$.

Answer:

A. $\frac{(x - 3)^2}{169}-\frac{(y + 2)^2}{81}=1$