Question

Find an equation in standard form for the hyperbola with vertices at (0, ±6) and asymptotes at
y=+-3/4x?

Answer 1

The vertices are on the y axis so the equation has this form:
\[\frac{y^2}{a^2}-\frac{x^2}{b^2}=1\]

Answer 2

a=6

Answer 3

The asymptotes are:
\[y=\frac{\pm a}{b}x\]

Answer 4

@Mertsj thank you!

Answer 5

yw

Answer 6

So
\[\frac{6}{b}=\frac{3}{4}\]

Answer 7

@Mertsj okay what is the next step?

Answer 8

What is b?

Answer 9

b=8

Answer 10

What is a^2?

Answer 11

a^2=36

Answer 12

What is b^2?

Answer 13

b^2=64

Answer 14

Write the equation.

Answer 15

so its y^2/36-x^2/64=1?

Answer 16

yes

Answer 17

@Mertsj thanks again!

Answer 18

yw