Calculus Answers

What is the equation of the hyperbola with vertices at (0, -4) and (0, 4) and foci at (0, -6) and (0, 6)

A: y^2 x^2
----- - ------ = 1
16 20

B: x^2 y^2
----- - -------- = 1
16 20

C: x^2 y^2
----- - ------ = 1
16 36

D: x^2 y^2
----- - -------- = 1
16 52

Graph this hyperbola

(x+3)^2 (y-2)^2
--------- - ---------- = 1
81 169

Graph this hyperbola

(y+3)^2 (x-2)^2
--------- - ---------- = 1
169 81

Graph this hyperbola

(x-3)^2 (y+2)^2
--------- - ----------- = 1
169 81

Graph this hyperbola

(y-3)^2 (x+2)^2
--------- - ----------- = 1
169 81

Graph this hyperbola

(y-2)^2 (x+1)^2
--------- - ----------- = 1
16 144

What are the equations for the asymptote of this hyperbola.

y^2 x^2
--- - ----- = 1?
36 121

A: y = 11 11
----- x, y = - ------- x
6 6

B: y = √85 √85
------ x, y = - ------- x
5 5

C: y = √157 √157
------ x, y = - -------- x
5 5

D: y = 6 6
---- x, y = - -------- x
11 11

The foci for the hyperbola (x-1)^2 (y+3)^2
-------- - --------- = 1 are (1 + √34, -3) and (1 - √34, -3)
25 9
A: True
B: False

5: The vertices for the hyperbola (x-1)^2 (y+3)^2
--------- - --------- = 1 are (1,0) and (1,-6)
25 9
A: True
B: False

4: What is the length of the conjugate axis?

(x-2)^2 (y+1)^2
-------- - --------- = 1
36 64

Answer: ______

3: What is the length of the transverse axis?

(x-2)^2 (y+1)^2
-------- - --------- = 1
36 64

Answer: _______

1: This is the equation of a horizontal hyperbola. (x-1)^2 (y+3)^2
-------- - -------------- = 1
25 9
A: True
B: False


2: Write the coordinates for the center of the hyperbola:

(y-2)^2 (x+1)^2
------- - --------- = 1
16 144

Answer: _________

Q. Draw the graph of following functions on graph paper.
(i) y=x
(ii) y=x+1
(iii)y=x-1
(iv)y=x+2
(v)y=2x
(vi)y=3x+5
(vii)y=-x+1
(viii)y=-x+2
(ix)y=-x
(x)y=-x-1