Hyperbola Properties and Equations

The video tutorial explains how to write the equation of a hyperbola in standard form. It begins by analyzing the equation and identifying the positive and negative terms. The process involves gathering terms, factoring, completing the square, and adjusting the equation to maintain equality. The tutorial then focuses on factoring perfect square trinomials and finalizing the equation in standard form. Finally, it determines the values of h, k, a, and b, explaining the significance of each in the context of the hyperbola's properties.

What indicates that the hyperbola has a vertical transverse axis?

• The x-squared term is positive.

• The equation is in the first form.

• The constant is on the left side.

• The y-squared term is positive.

What is the greatest common factor factored out from the y-part of the equation?

• 16

• 8

• 4

• 2

When completing the square for y-squared plus 8y, what constant is added inside the parentheses?

• 16

• 12

• 20

• 8

What is the result of subtracting 81 from the right side of the equation?

• The equation becomes a circle.

• The equation becomes a parabola.

• The equation becomes unbalanced.

• The equation remains balanced.

What are the binomial factors of y-squared plus 8y plus 16?

• (y + 3)(y + 3)

• (y + 4)(y + 4)

• (y + 5)(y + 5)

• (y + 2)(y + 2)

What is the simplified form of the equation after dividing by 36?

• The square of y plus 4 divided by 9 minus the square of x plus 3 divided by 4 equals 1.

• The square of y plus 3 divided by 4 minus the square of x plus 4 divided by 9 equals 1.

• The square of y plus 4 divided by 4 minus the square of x plus 3 divided by 9 equals 1.

• The square of y plus 3 divided by 9 minus the square of x plus 4 divided by 4 equals 1.

What is the value of h in the standard form equation?

• 3

• -3

• 4

• -4

What is the value of k in the standard form equation?

• -4

• 3

• 4

• -3

What is the value of a in the standard form equation?

• 5

• 4

• 3

• 2

What is the value of b in the standard form equation?

• 2

• 1

• 4

• 3