Equations of Hyperbolas

Question 1

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

Revolt · Accepted Answer

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

Question 2

510✔ 1224

Revolt · Accepted Answer

✔ 12

Question 3

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 4

centerfocus✔ vertex

Revolt · Accepted Answer

vertex

Question 5

✔ centerfocusvertex

Revolt · Accepted Answer

center

Question 6

(a – c)(c + a)✔ (c – a)

Revolt · Accepted Answer

(c – a)

Equations of Hyperbolas Answers

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