Question

A hyperbola has vertices (0,–6) and (0,6) and asymptotes y=3/4x and y=-3/4x .
What does the asymptote have to do with this?
Part I: In what direction is this hyperbola oriented? (2 points)


Part II: What are the coordinates of the center of this hyperbola? (2 points)


Part III: What are the values of a and b for this hyperbola? (4 points)


Part IV: Write the equation of this hyperbola. (4 points)

Answer 1

I don't understand why there's 2 asymptotes? Why is one negative?

Answer 2

since u know the vertices u know the value of a*e

Answer 3

also the equation of the asymptote is :
\[y=\frac{ b }{ a }x \]
and \[y=-\frac{ b }{ a }x\]

Answer 4

so now u can find out the equation of the hyperbola and pretty much all the other answers

Answer 5

u are actually using the asymptotes to find the values of a and b

Answer 6

@prathamesh_M Thank you! Shouldn't this be a vertical hyperbola?
Also, what's the difference between that negative sign for the asymptote?

Answer 7

It's negative because there's 2 asymptotes that cross each other so one will always have a negative slope

Answer 8

(0,0) should be the center..
a=3, b=4

equation should be \[y^2/16-x^2/9=1\]

Answer 9

@Thatonegirl_

Are the value of the two asymptotes always the same?

Answer 10

except one is just negative?

Answer 11

Yup, so just disregard the positive or negative when working with it

Answer 12

thank you. Is my answer correct?

Answer 13

No problem. And give me a min, I've studied these conics at least 3 times and always forget them right after xD

Answer 14

It's okay, take your time. Thank you so much :D