Question

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

Answer 1

We have

$\frac{x^2}{25}-\frac{y^2}{49}=1$

we will follow the next form

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

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

$y=\pm\frac{b}{a}x$

in our case

a=5

b=7

then we substitute the values

$y=\pm\frac{7}{5}x$

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