Understanding Hyperbolas: From Equation to Graph

The video tutorial explains how to write the equation of a hyperbola in standard form. It begins by identifying the characteristics of the hyperbola equation, such as the positive x-squared term and negative y-squared term, indicating a horizontal transverse axis. The tutorial then guides through rearranging the equation, factoring out common factors, and completing the square for both x and y terms. It concludes by simplifying the equation to its standard form and identifying key parameters like h, k, a, and b.

What does the positive x squared term and negative y squared term in a hyperbola's equation indicate about its graph?

• The hyperbola opens upwards and downwards.

• The hyperbola has no real graph.

• The hyperbola opens to the left and right.

• The hyperbola is a circle.

What is the first step in rearranging the given hyperbola equation?

• Divide all terms by the constant.

• Group x and y terms separately and move the constant to the right.

• Multiply all terms by a common factor.

• Add a constant to both sides.

When factoring the x terms, what is the greatest common factor used?

• 5

• 10

• 36

• 25

What is the purpose of completing the square in the context of this hyperbola equation?

• To rewrite the equation in standard form.

• To eliminate the constant term.

• To convert the equation into a circle.

• To simplify the equation.

What value is added inside the parentheses when completing the square for x squared minus 10x?

• 25

• 15

• 5

• 10

How is the equation adjusted after completing the square for y squared plus 8y?

• Add 16 to both sides.

• Subtract 400 from both sides.

• Subtract 16 from both sides.

• Add 400 to both sides.

What is the final form of the hyperbola equation after simplification?

• (x + 5)^2/25 + (y - 4)^2/36 = 1

• (x - 5)^2/36 + (y + 4)^2/25 = 1

• (x + 5)^2/36 - (y - 4)^2/25 = 1

• (x - 5)^2/25 - (y + 4)^2/36 = 1

What is the value of h in the final hyperbola equation?

• -5

• 5

• 4

• -4

What is the value of k in the final hyperbola equation?

• -5

• -4

• 5

• 4

What are the values of a and b in the final hyperbola equation?

• a = 5, b = 4

• a = 4, b = 5

• a = 5, b = 6

• a = 6, b = 5