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.
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.
Answers
Reiny
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.
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.
moony
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
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
On my way
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
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