Write the equation of a hyperbola given the eccentricity

The video tutorial explains the concepts of center and HK values, eccentricity, and their relation to C and A. It involves problem-solving to find the values of A and B, discusses the focal and transverse axes, and concludes with setting up the final equation. The tutorial aims to clarify these mathematical concepts through step-by-step explanations.

What is the center of the hyperbola as mentioned in the video?

• (4, 1)

• (2, 3)

• (0, 0)

• (1, 4)

How is eccentricity defined in relation to C and A?

• A^2/C^2

• C^2/A^2

• A/C

• C/A

If the eccentricity is 2 and C is 6, what is the value of A?

• 3

• 6

• 2

• 12

What is the relationship between a^2, b^2, and c^2 in the context of the hyperbola?

• a^2 - b^2 = c^2

• a^2 + b^2 = c^2

• c^2 - a^2 = b^2

• b^2 - a^2 = c^2

What is the equation of the hyperbola as derived in the video?

• (x+1)^2/9 - (y+4)^2/27 = 1

• (x+4)^2/9 - (y-1)^2/27 = 1

• (x-1)^2/9 - (y-4)^2/27 = 1

• (x-1)^2/27 - (y-4)^2/9 = 1