A hyperbola is centered at C=(3,7). The vertices are (9,7) and (-3,7). The slopes of the asymptotes are m=+-5/6

Question

A hyperbola is centered at C=(3,7). The vertices are (9,7) and (-3,7). The slopes of the asymptotes are m=+-5/6.

 

Answer 1

If you make a plot of the veritices and the center, you find----

 

The axis of the hyperbola is horizontal.

 

Since center is (3,7)

 

a=9-3=6

 

Since equation of asymptote is +-5/6 =. +-b/a

 

So, b= 5

 

 

 

So, the equation of hyperbola is 

 

  ((x-3)^2)/36.   -  ((y-7)^2)/25. =1