Learn to write the equation of a hyperbola given vertices and the foci

The video tutorial explains how to derive the equation of a hyperbola by plotting vertices and identifying the transverse axis. It covers the calculation of parameters A, B, and C, and demonstrates how to finalize the hyperbola equation. The tutorial emphasizes the differences between parabolas, ellipses, and hyperbolas, and uses the Pythagorean theorem analogy to explain the relationship between A, B, and C.

What is the first step in determining the type of hyperbola equation to write?

• Graph the hyperbola

• Determine the center

• Plot the given information

• Calculate the foci

How do you determine the center of a hyperbola?

• By finding the midpoint between the vertices

• By calculating the average of the x-coordinates of the vertices

• By using the distance between the vertices

• By finding the midpoint between the foci

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

• c^2 = a^2 - b^2

• a^2 = b^2 + c^2

• b^2 = a^2 + c^2

• c^2 = a^2 + b^2

If 'a' is 5 and 'c' is sqrt(26), what is the value of 'b'?

• 4

• 3

• 2

• 1

What is the final equation of the hyperbola given 'a' is 5 and 'b' is 1?

• x^2/1 + y^2/25 = 1

• x^2/25 + y^2/1 = 1

• x^2/1 - y^2/25 = 1

• x^2/25 - y^2/1 = 1