How to write the equation of a hyperbola given the foci and vertices

The video tutorial guides students through writing an equation for a hyperbola. It begins with setting up the problem by identifying key points such as foci, vertices, and the center. The teacher explains the importance of sketching the information and identifying the vertical transverse axis. The tutorial then covers calculating parameters A and B using the equation C^2 = A^2 + B^2. Finally, the teacher demonstrates how to write the equation by plugging in the calculated values, emphasizing the placement of A and B under the correct variables.

What is the first step recommended when solving a hyperbola equation problem?

• Determine the transverse axis

• Find the center of the hyperbola

• Sketch the information

• Calculate the distance between foci

What is the center of the hyperbola given the vertices (-1, 2) and (-1, -2)?

• (-1, 0)

• (1, 0)

• (0, -1)

• (-1, 1)

How is 'a' defined in the context of a hyperbola?

• Distance from center to foci

• Distance from center to vertices

• Distance between the foci

• Distance between the vertices

Which equation is used to find 'b' in a hyperbola?

• C^2 = a^2 - b^2

• C^2 = a^2 + b^2

• C^2 = a^2 * b^2

• C^2 = b^2 - a^2

In the equation of a hyperbola, where should 'a^2' be placed if the transverse axis is vertical?

• Under the y-term

• It doesn't matter

• Under both terms

• Under the x-term