Conic Sections Review

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

• (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center.

• (y - k)²/a² - (x - h)²/b² = 1, where (h, k) is the center.

• (x + h)²/a² + (y + k)²/b² = 1, where (h, k) is the center.

• (x - h)²/b² - (y - k)²/a² = 1, where (h, k) is the center.

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

• c² = a² + b², where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.

• c² = a² - b², where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.

• c² = a² + 2b², where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.

• c² = 2a² + b², where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.

What are the coordinates of the foci for the hyperbola y²/12 - x²/5 = 1?

• (0, ±√12)

• (0, ±√17)

• (±√5, 0)

• (±√17, 0)

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

• (y - k)²/a² - (x - h)²/b² = 1, where (h, k) is the center.

• (x - h)²/a² - (y - k)²/b² = 1, where (h, k) is the center.

• (y - k)²/b² - (x - h)²/a² = 1, where (h, k) is the center.

• (x - h)²/b² - (y - k)²/a² = 1, where (h, k) is the center.

How do you graph a hyperbola?

• Identify the center, vertices, foci, and asymptotes, then sketch the curves approaching the asymptotes.

• Draw a straight line through the center and vertices.

• Plot points randomly on the graph until a curve forms.

• Use a compass to draw a perfect circle around the center.

What is the equation of a hyperbola centered at (h, k) with a horizontal transverse axis?

• (x - h)²/a² - (y - k)²/b² = 1

• (y - k)²/a² - (x - h)²/b² = 1

• (x - h)²/b² - (y - k)²/a² = 1

• (x - h)²/a² + (y - k)²/b² = 1

What is the significance of the transverse axis in a hyperbola?

• It is the line segment that connects the vertices of the hyperbola and determines its orientation.

• It is the line that bisects the hyperbola into two equal parts.

• It represents the distance between the foci of the hyperbola.

• It is the axis that defines the asymptotes of the hyperbola.

What is the equation of a hyperbola centered at (h, k) with a vertical transverse axis?

• (y - k)²/a² - (x - h)²/b² = 1

• (x - h)²/a² - (y - k)²/b² = 1

• (y - k)²/b² - (x - h)²/a² = 1

• (x - h)²/b² - (y - k)²/a² = 1

How do you determine if a hyperbola is vertical or horizontal?

• If the equation is in the form (y - k)²/a² - (x - h)²/b² = 1, it is vertical.

• If the equation is in the form (x - h)²/a² - (y - k)²/b² = 1, it is horizontal.

• If the equation is in the form (y - k)²/b² - (x - h)²/a² = 1, it is vertical.

• If the equation is in the form (x - h)²/b² - (y - k)²/a² = 1, it is horizontal.

What is a conic section?

• A type of triangle

• A curve obtained by intersecting a cone with a plane

• A geometric shape with four sides

• A linear equation in two variables