Hyperbolas

Question 1

Horizontal Case of a Hyperbola

Answer 1

Hyperbolas open left and right

Question 2

Vertical Case of a Hyperbola

Answer 2

Hyperbolas open up and down

Question 3

Asymptotes

Answer 3

Lines that act as boundaries for the hyperbolas

Question 4

Transverse Axis

Answer 4

Like the major axis of an ellipse, the center, vertices, and foci lie on it

• the vertex is between the center and focus
• The Transverse Axis = 2a

Question 5

Conjugate Axis

Answer 5

Like the minor axis of an ellipse, the co-vertices lie on it

-The Conjugate Axis = 2b

Question 6

Standard Form of a Horizontal Ellipse at (0,0)

Answer 6

x^2/a^2 - y^2/b^2 = 1

Question 7

Standard Form of a Vertical Ellipse at (0,0)

Answer 7

y^2/a^2 - x^2/b^2 = 1

Question 8

Standard Form of a Horizontal Ellipse at (h,k)

Answer 8

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

Question 9

Standard Form of a Vertical Ellipse at (h,k)

Answer 9

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

Question 10

Vertices

Answer 10

Vertices lie on the Transverse Axis and are + or - a from the center

Question 11

Foci

Answer 11

Foci lie on the Transverse Axis and are + or - c from the center

Question 12

Slope of the Asymptotes for a Horizontal Hyperbola

Answer 12

m = + or - b/a

-Slope is counted from the center (either (0,0) or (h,k)

Question 13

Slope of the Asymptotes for a Vertical Hyperbola

Answer 13

m = + or - a/b

-Slope is counted from the center (either (0,0) or (h,k)

Question 14

Horizontal vs. Vertical?

Answer 14

There is no relationship between a^2 and b^2 (a^2 can be less than or equal to b^2), so look at the x^2 and y^2 for whether the Hyperbola is Horizontal or Vertical

1. If x^2 is first, the Hyperbola is Horizontal (along the X-axis)
2. If y^2 is first, the Hyperbola is Vertical (along the Y-axis)

Question 15

Identifying a Hyperbola from its General Form Equation

Answer 15

1. It has 2 squared terms (#x^2 and #y^2)

2. Its two squared numbers have opposite signs (One number is negative, one number is positive)