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

The video tutorial revisits problems related to ellipses, focusing on plotting foci and determining the center. It explains the concept of transverse and conjugate axes, and how to calculate distances such as C squared. The instructor derives the equation of a hyperbola, emphasizing the importance of understanding a squared and b squared. The session concludes with final calculations and a summary of the process.

What is the first step in solving problems related to ellipses?

• Finding the center

• Sketching the information

• Calculating the foci

• Determining the transverse axis

What does the vertical orientation of the transverse axis imply in the context of the hyperbola?

• a^2 is under x

• b^2 is under y

• a^2 is under y

• b^2 is under x

If the distance from the center to the foci is 8, what is the value of C^2?

• 64

• 48

• 32

• 16

How is the conjugate axis length related to the value of b?

• It is equal to b

• It is twice the value of b

• It is half the value of b

• It is unrelated to b

What is the final equation of the hyperbola derived in the lesson?

• y^2 / 48 + x^2 / 16 = 1

• y^2 / 16 - x^2 / 48 = 1

• y^2 / 48 - x^2 / 16 = 1

• x^2 / 48 - y^2 / 16 = 1