Question

A hyperbola is represented by the equation x^2/9 - (y - 1)^2 = 1. Identify the asymptotes of the graph.

Out of the options I'm given, it's either these two:

y = (sqrt5/3) x + 1 and y = -(sqrt5/5) x + 1
y = (sqrt5/3) (x + 1) and y = -(sqrt5/5) (x + 1)

The answer I keep coming up with is y = (xsqrt5/3) + 1 and y = -(xsqrt5/5) + 1, so I don't know where I'm wrong and what option to pick.

Answer 1

Your hyperbola has centre (0,1) , a = 3, and b = 1
vertices would be (3,1) and (-3,1)

To sketch this hyperbola I would faintly sketch a rectangle with corners at (3,2), (-3,2) , (-3,0) and (3,0)
One asymptote would run through (3,2) and (-3,0) and of course (0,1)
slope = 1/3
y = (1/3)x + 1 , since (0,1) is the y-intercept
similarly the other one would be y = (-1/3)x + 1

verification:
http://www.wolframalpha.com/input/?i=plot+x%5E2%2F9+-+(y+-+1)%5E2+%3D+1,+y+%3D+(1%2F3)x+%2B+1,+y+%3D+(-1%2F3)x+%2B+1

I have no idea where the square roots come from in your choices.

Answer 2

y= sqrt5/3 x+1 and y= -sqrt5/3 x+1
no parentheses
if you’re doing the comic sections test i got
1. c 2sqrt10
2. ellipse
3. a. (0,-4) r=sqrt 3
4. b (x+3)^2 +(y-2)^2=9
5. d (x-4)^2+(y-3)^2=4
6. a. (x-3)^2/16 + (y-1)^2/4=1
7. c. (x+4)^2/4 +(y+3)^2/16 =1 (-4,-3 +- 2 sqrt3)
8. ellipse is vertical because a<b
9. a 152 million
10. c x^2/3
11. d (y-5)^2= 3(x-1)
12. c focus (4,3)
13. i got this one wrong so don’t pick 4
14. graph b should look like ) • ( where the center dot is on (5,2) and the other dots are at (1,2) and (9,2)
15. a (y+5)^2/9 - (x-2)^2/3 =1
16. a y= sqrt5/3 x+1 and y= -sqrt5/3 x+1
good luck

Answer 3

Moony has some wrong answers due to having different q's or typing wrong. Thus, the correct answers for those have questions like me

1. 2sqrt13
2. ellipse
3. C (0,-3) r=sqrt5
4. C x+1^2 y-4^2=1
5. D x-4 y+3=4
6. A x-3/16 + y-1/4
7. C (x+4)^2/4 +(y+3)^2/16 =1 (-4,-3 +- 2 sqrt3)
8. vertical
9. Ans: 152 If the sun is located at one focus and its coordinates are left-parenthesis 0,0 right-parenthesis, find Earth's farthest distance from the sun in millions of kilometers.

10. D x^2/3
11. C y-5=-3(x-1
12. focus 2,1 dir=6
13. Ans:4
A parabolic microphone used on the sidelines of a professional football game uses a reflective dish 16 in. wide and 4 in. deep. How far from the bottom of the dish should the microphone be placed?

14. Graph B as moony has mentioned 5,2 center

15. B y+3/25 - x-1/25 =1

16. A y= sqrt5/3 x+1 and y= -sqrt5/3 x+1