Understanding Hyperbolas

What is the definition of a hyperbola?

• A set of points equidistant from a single point.

• A set of points equidistant from a line.

• A set of points where the sum of distances to two fixed points is constant.

• A set of points where the difference of distances to two fixed points is constant.

What is the purpose of taking the absolute value in the definition of a hyperbola?

• To ensure the distance is always negative.

• To ensure the distance is always zero.

• To ensure the distance is always positive.

• To ensure the distance is always constant.

How does the transverse axis affect the orientation of a hyperbola?

• It determines whether the hyperbola opens left-right or up-down.

• It determines the number of foci.

• It determines the size of the hyperbola.

• It determines the color of the hyperbola.

What is the orientation of a hyperbola with a horizontal transverse axis?

• It is a line.

• It opens up and down.

• It opens left and right.

• It is a circle.

How does the equation of a hyperbola differ from that of an ellipse?

• The hyperbola equation uses multiplication, while the ellipse uses division.

• The hyperbola equation uses subtraction, while the ellipse uses addition.

• The hyperbola equation uses addition, while the ellipse uses subtraction.

• Both equations are identical.

What is the relationship between c^2, a^2, and b^2 in a hyperbola?

• c^2 = a^2 + b^2

• c^2 = a^2 - b^2

• c^2 = a^2 / b^2

• c^2 = a^2 * b^2

In the standard form of a hyperbola, what do H and K represent?

• The coefficients of x and y.

• The center of the hyperbola.

• The vertices of the hyperbola.

• The foci of the hyperbola.

How are the vertices of a hyperbola determined in its standard form?

• By adding and subtracting the b value from the center.

• By adding and subtracting the a value from the center.

• By adding and subtracting the d value from the center.

• By adding and subtracting the c value from the center.

Where are the foci located in a hyperbola with a vertical transverse axis?

• At the origin.

• At the vertices.

• Along the y-axis.

• Along the x-axis.

What changes in the standard form equation when the transverse axis is vertical?

• The x and y terms are swapped.

• The equation becomes a circle.

• The equation becomes a line.

• The equation remains unchanged.