Understanding Hyperbolas

The video tutorial explains how to determine which graph represents the hyperbola given by the equation y^2/9 - x^2/4 = 1. It discusses the center of the hyperbola, which is at (0,0), and how to determine the direction it opens by identifying the positive term in the equation. The tutorial also covers solving the equation to find the vertices and concludes by justifying the correct graph choice based on these calculations.

What is the main task in the problem presented in the video?

• Identifying the correct graph for a given hyperbola equation.

• Solving a quadratic equation.

• Finding the area of a circle.

• Calculating the slope of a line.

Where is the center of the hyperbola located in the given equation?

• (2, 2)

• (0, 0)

• (1, 1)

• (3, 3)

What is the significance of the center in the hyperbola equation?

• It determines the slope of the hyperbola.

• It is the midpoint of the vertices.

• It is the point from which the hyperbola is symmetric.

• It is irrelevant to the graph.

How can you determine the direction in which a hyperbola opens?

• By calculating the distance between the foci.

• By identifying the positive term in the equation.

• By checking the coefficients of the terms.

• By looking at the negative term in the equation.

Why does the positive term in the hyperbola equation determine its direction?

• Because it is always larger than the negative term.

• Because it indicates the axis of symmetry.

• Because it simplifies the equation.

• Because it allows setting the other term to zero.

What happens when you set the x term to zero in the given hyperbola equation?

• You find the y-intercepts.

• You find the x-intercepts.

• You determine the slope.

• You calculate the area.

If the x term were positive, in which direction would the hyperbola open?

• Up and down

• Left and right

• Diagonally

• It would not open

What are the coordinates of the vertices on the hyperbola?

• (±2, 0)

• (0, ±3)

• (0, ±2)

• (±3, 0)

Which graph correctly represents the hyperbola based on the vertices?

• Graph A

• Graph B

• Graph C

• Graph D

Why can't the hyperbola open left and right in this case?

• Because the x term is negative.

• Because the y term is larger.

• Because the center is at (0, 0).

• Because the equation is not in standard form.