Hyperbolas

Question 1

What does F1 and F2 represent on a hyperbola?

Answer 1

The foci

Question 2

What does P represent on a hyperbola?

Answer 2

A point given

Question 3

What does k represent?

Answer 3

|PF1 - PF2|
Constant difference

Question 4

What is the constant difference also equal to?

Answer 4

2a

Question 5

What is the equation of a hyperbola that opens left or right?

Answer 5

((x-h)^2 / a^2) - ((y-k)^2 / b^2) = 1

Question 6

What is the equation of a hyperbola that opens up or down?

Answer 6

((y-k)^2 / a^2) - ((x-h)^2 / b^2) = 1

Question 7

What is the transverse axis?

Answer 7

The line that passes through the center, vertices, and foci

Question 8

What is the length of the transverse axis?

Answer 8

2a

Question 9

What is the conjugate axis?

Answer 9

Perpendicular to the traverse axis

Question 10

What is the length of the conjugate axis?

Answer 10

2b

Question 11

What is the a?

Answer 11

Center to vertex

Question 12

What is the c?

Answer 12

Center to focus

Question 13

What is the eccentricity of a hyperbola?

Answer 13

e or c/a > 1

Question 14

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

Answer 14

c^2 = a^2 + b^2

Question 15

What is the equation for the asymptotes of a hyperbola opening left or right?

Answer 15

y - k = ±b/a(x-h)

Question 16

What is the equation for the asymptotes of a hyperbola opening up or down?

Answer 16

y - k= ±a/b(x-h)

Question 17

What is the equation for the directrices of a hyperbola opening left or right?

Answer 17

x = h ± a / e

Question 18

What is the equation for the directrices of a hyperbola opening up or down?

Answer 18

y = k ± a / e

Question 19

For a hyperbola centered at the origin, what is the equation for a tangent line at point (x1, y1)?

Answer 19

(xx1 / a^2) - (yy1/b^2) = 1