How to write the equation of a hyperbola given the asymptotes and vertical transverse axis

The video tutorial covers the topic of hyperbolas, focusing on the vertical transverse axis. It explains the equation of hyperbolas, emphasizing the importance of memorizing the formula as it won't be available during tests. The tutorial also discusses the concept of asymptotes and how to derive their equations. It guides students through solving for variables A, B, H, and K, providing a step-by-step approach to formulating the final equation. The session concludes with a Q&A segment to clarify any doubts.

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

• x^2/b^2 - y^2/a^2 = 1

• y^2/b^2 - x^2/a^2 = 1

• y^2/a^2 - x^2/b^2 = 1

• x^2/a^2 - y^2/b^2 = 1

Which of the following is the correct equation for the asymptotes of a hyperbola with a vertical transverse axis?

• x = ±(a/b)(y - k) + h

• y = ±(b/a)(x - h) + k

• y = ±(a/b)(x - h) + k

• x = ±(b/a)(y - k) + h

In the context of hyperbolas, what does the variable 'a' represent when the transverse axis is vertical?

• The distance from the center to a focus along the y-axis

• The distance from the center to a vertex along the x-axis

• The distance from the center to a vertex along the y-axis

• The distance from the center to a focus along the x-axis

If the asymptote equation is given as y = ±(5/4)(x + 2) + 3, what is the value of 'h'?

• -2

• 3

• -3

• 2

Given the asymptote equation y = ±(5/4)(x + 2) + 3, what is the value of 'k'?

• -3

• 2

• -2

• 3