Given the vertices and focus find the standard form of the hyperbola

The video tutorial explains how to find the standard form of a hyperbola by using two different formulas based on whether the transverse axis is horizontal or vertical. It involves graphing given points to determine the axis, finding the center, and calculating the values of A, B, and C. The tutorial concludes with writing the equation for a horizontal transverse axis and finalizing the hyperbola equation.

What are the two possible orientations for the transverse axis of a hyperbola?

• Horizontal and diagonal

• Vertical and diagonal

• Horizontal and vertical

• Vertical and circular

How do you determine the orientation of the transverse axis from the graph?

• By measuring the length of the transverse axis

• By observing the alignment of the vertices and foci

• By checking the distance between the foci

• By calculating the midpoint of the vertices

Where is the center of a hyperbola located?

• At the midpoint of the conjugate axis

• At the midpoint between the foci

• At the midpoint of the transverse axis

• At the intersection of the asymptotes

What is the formula for the distance 'a' in a hyperbola?

• The distance from the center to a focus

• The distance from the center to a vertex

• The distance between the foci

• The distance between the vertices

How is the value of 'b' determined in a hyperbola?

• By adding the square of 'a' to the square of 'c'

• By multiplying the square of 'a' with the square of 'c'

• By subtracting the square of 'a' from the square of 'c'

• By dividing the square of 'c' by the square of 'a'

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

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

• a^2 = b^2 + c^2

• b^2 = a^2 - c^2

What is the standard form equation of a hyperbola with a horizontal transverse axis?

• (y-k)^2/b^2 - (x-h)^2/a^2 = 1

• (x-h)^2/a^2 - (y-k)^2/b^2 = 1

• (y-k)^2/a^2 - (x-h)^2/b^2 = 1

• (x-h)^2/b^2 - (y-k)^2/a^2 = 1