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

The video tutorial explains how to plot and analyze conic sections, focusing on hyperbolas. It covers identifying the center using foci, determining key components like HK, A, B, and C, and solving for B^2. The tutorial concludes with writing the hyperbola equation, emphasizing the importance of the vertical transverse axis.

What is the first step in analyzing a conic section like a hyperbola?

• Plot the given information

• Calculate the length of the transverse axis

• Find the value of a

• Determine the orientation of the hyperbola

How is the center of a hyperbola determined?

• It is the midpoint of the major axis

• It is the midpoint of the vertices

• It is the midpoint of the foci

• It is the midpoint of the transverse axis

What does the length of the transverse axis help determine?

• The value of c

• The orientation of the hyperbola

• The value of a

• The value of b

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

• Under the x term

• Under both x and y terms

• It does not matter

• Under the y term

What is the final form of the hyperbola equation when the transverse axis is vertical?

• x^2/b^2 - y^2/a^2 = 1

• y^2/a^2 - x^2/b^2 = 1

• y^2/b^2 - x^2/a^2 = 1

• x^2/a^2 - y^2/b^2 = 1