Write the equation of a hyperbola given the foci and length of transverse axis

The video tutorial explains how to plot points and identify the transverse axis, focusing on determining whether it is horizontal or vertical. It covers labeling foci and vertices, calculating distances A, B, and C, and using these to derive the hyperbola equation. The tutorial emphasizes the importance of understanding the differences between hyperbola and ellipse formulas and provides a step-by-step guide to writing the final equation.

What is the primary purpose of plotting points when analyzing a hyperbola?

• To calculate the area of the hyperbola

• To find the length of the transverse axis

• To identify the orientation of the transverse axis

• To determine the color of the graph

How is the center of a hyperbola determined?

• By finding the midpoint between the vertices and foci

• By measuring the distance from the origin

• By calculating the average of all plotted points

• By using the formula a^2 + b^2 = c^2

What is the relationship between 'a', 'b', and 'c' in a hyperbola?

• a^2 = b^2 + c^2

• c^2 = a^2 + b^2

• b^2 = a^2 - c^2

• a^2 = c^2 - b^2

In the equation of a hyperbola, why is the x-term placed over 'a' in this example?

• Because the transverse axis is vertical

• Because the transverse axis is horizontal

• To simplify the equation

• To match the previous problem's format

What distinguishes the formula for hyperbolas from that of ellipses?

• The use of addition instead of subtraction

• The order of terms based on the transverse axis

• The inclusion of a constant term

• The use of multiplication instead of division