Question

Graph the hyperbola x^2/25-y^2/49=1. What are the equations of the asymptotes?

Answer 1

We have

`(x^2)/(25)-(y^2)/(49)=1`

we will follow the next form

`(x^2)/(a^2)-(y^2)/(b^2)=1`

For the equations of the asymptotes, we will follow the next formula

`y=\pm(b)/(a)x`

in our case

a=5

b=7

then we substitute the values

`y=\pm(7)/(5)x`

Then we have the next graph

where the graph green is the hyperbola and the lines in purple and black are the asymptotes

ANSWER

y=7/5x

y=-7/5x