Conic Sections and Hyperbolas Quiz

The video tutorial covers the identification and graphing of a hyperbola from a given equation. It begins with grouping terms, identifying the conic section, completing the square, and finally graphing the hyperbola with its asymptotes. The tutorial provides a step-by-step approach to solving the problem, emphasizing the importance of completing the square and understanding asymptotes.

What is the first step in solving the conic section problem presented in the video?

• Graphing the equation

• Grouping x and y terms on one side

• Identifying the type of conic section

• Finding the asymptotes

What type of conic section is identified in the problem?

• Hyperbola

• Circle

• Parabola

• Ellipse

What is the purpose of completing the square in this problem?

• To simplify the equation

• To find the center of the hyperbola

• To transform the equation into standard form

• To determine the asymptotes

What is the center of the hyperbola in the standard form equation?

• (2, -1)

• (0, 0)

• (1, -2)

• (-1, 2)

How are the asymptotes of the hyperbola determined?

• By using the slopes derived from the standard form

• By solving for x and y

• By finding the intercepts

• By graphing the equation

What is the significance of the asymptotes in the graph of a hyperbola?

• They are the points where the graph intersects

• They are the lines the graph approaches but never touches

• They are the maximum and minimum points

• They are the axes of symmetry

What happens to the graph of the hyperbola as x approaches positive or negative infinity?

• It approaches the asymptotes

• It forms a circle

• It becomes a straight line

• It intersects the asymptotes

What is the slope of the asymptotes for the hyperbola centered at (-1, 2)?

• 1/2

• 2/5

• 5/2

• 3/2

Which term in the equation indicates the hyperbola opens vertically?

• The linear term

• The constant term

• The y squared term

• The x squared term

What is the final step in graphing the hyperbola?

• Finding the intercepts

• Drawing the asymptotes

• Completing the square

• Identifying the center