how to sketch the graph of a hyperbola in conic sections

The video tutorial explains how to rewrite a hyperbola equation in conic section form, identify key parameters (a, b, c), and determine the center of the hyperbola. It covers finding the transverse axis, vertices, and foci, and provides tips for estimating square roots. The tutorial concludes with instructions on graphing asymptotes and sketching the hyperbola.

What is the value of 'a' if a^2 is 4 in the context of a hyperbola?

• 1

• 4

• 2

• 3

How do you determine the center of a hyperbola?

• By calculating the average of a and b

• By using the distance formula

• By using the values of h and k

• By finding the midpoint of the vertices

What is the orientation of the transverse axis if a^2 is under x?

• Diagonal

• Undefined

• Horizontal

• Vertical

How do you find the vertices of a hyperbola?

• By finding the midpoint of the foci

• By calculating the average of h and k

• By adding and subtracting 'a' from the center

• By using the distance formula

What is the approximate value of the square root of 5?

• Between 3 and 4

• Between 2 and 3

• Between 1 and 2

• Exactly 2.5

What is the equation of the asymptotes for a hyperbola with a horizontal transverse axis?

• y = ±(b/a)(x - h) + k

• y = ±(a/b)(x - h) + k

• y = ±(b/a)(x + h) - k

• y = ±(a/b)(x + h) - k

What is the purpose of creating a box when graphing asymptotes?

• To calculate the distance between foci

• To aid in drawing the asymptotes

• To determine the length of the transverse axis

• To find the center