Equations of Hyperbolas

Question 1

Which statements about the hyperbola are true? Check all that apply.

Revolt · Accepted Answer

A: The center is located at (0, 0).; B: There is a vertex at (–6, 0).; E: The directrices are vertical lines.

Question 2

The center of a hyperbola is located at (0, 0). One focus is located at (0, 5) and its associated directrix is represented by the line y = . Given the standard form of the equation of a hyperbola, what are the values of a and b?

Revolt · Accepted Answer

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of .: 2a; 2a is used in the equation because the is a point on the hyperbola and it is the difference in the distances from this point to the foci.: vertex; This can be shown algebraically if we let a be the distance from the to the vertex. Then, the difference of the distances is (c + a) – .: center; This can be shown algebraically if we let a be the distance from the to the vertex. Then, the difference of the distances is (c + a) – .: (c – a)

Question 3

Which equation represents the graph?

Revolt · Accepted Answer

A: Option A

Question 4

A hyperbola has a center at the origin, a vertex at (9, 0), and a focus at (41, 0). What is the equation of the hyperbola?

Revolt · Accepted Answer

A:

Question 5

Question 5

Revolt · Accepted Answer

121963

Question 6

Which statements about the hyperbola are accurate? Check all that apply.

Revolt · Accepted Answer

B: There is a focus at (0, 15).; C: y = x is an asymptote.; E: y = is a directrix.

Question 7

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of .

Revolt · Accepted Answer

B: 2a

Question 8

Question 8

Revolt · Accepted Answer

4

Question 9

centerfocus✔ vertex

Revolt · Accepted Answer

C: vertex

Question 10

✔ centerfocusvertex

Revolt · Accepted Answer

A: center

Equations of Hyperbolas Answers

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