Question

Find an equation in standard form for the hyperbola with vertices at (0,+-6) and asymptotes at y=+-3/5x
Please explain the steps!

Answer 1

@satellite73

Answer 2

can you start out with telling us the center, and the general setup for the hyperbolic equation?

Answer 3

the center would have to be (0,0). and well it would have to be y-k^2/a^2 - x-h^2/b^2=1 @amistre64

Answer 4

so far so good

lets clean that up to be: (y/b)^2 - (x/a)^2 = 1

i like to keep my yb parts together and xa parts together, it helps with the asymptote information

Answer 5

the slope of the asymptote is defined in as b/a

we know b as the length from the center to the vertex in this case; so that should be 6 agreed?

Answer 6

from this we can determine that:\[\frac ba=\frac 35\]
\[\frac 6a=\frac 35\]
solve for a to finish the equation

Answer 7

\[\frac{y^2}{b^2}-\frac{x^2}{a^2}=1\]
\[\frac{y^2}{6^2}-\frac{x^2}{a^2}=1\]

Answer 8

Can you explain how you got the 3/5? @amistre64

Answer 9

i simply read the information in the problem ....

Answer 10

Oh yes! sorry hahahahah. Thank you. Now I have answer choices, and the only answer choice it seems to fit would be y^2/36-x^2/100?

Answer 11

well, since a = 10, id have to agree :)

Answer 12

I had originally picked y^2/36-x^2/25 but i got it wrong

Answer 13

you assumed the slope of the asymptote used exact values of b and a, instead of sclaed values

Answer 14

*scaled values

Answer 15

Thank you once again :D