Find an Equation of the Hyperbola Centered at the Origin $( \pm 4,0 )$

question 19

Multiple Choice

Find an equation of the hyperbola centered at the origin that satisfies the given condition. Vertices: $( \pm 4,0 )$ , asymptotes: $y = \pm \frac { 7 } { 4 } x$

• A) \(\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1\)
• B) \(\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1\)
• C) \(\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1\)
• D) \(\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1\)

---

Definitions:

Linear Regression Equation

An equation that describes the relationship between a dependent variable and one or more independent variables using a straight line.

Horizontal Line

In a graph or diagram, a straight line that runs left to right parallel to the x-axis, indicating a constant value.

Relationship

The way in which two or more concepts, objects, or people are connected, or the state of being connected.

Slope

The measure of the steepness or incline of a line, indicating the rate of change between two variables.