Question

vertices(+ or - 7 ,o) , e = 4/3

Answer 1

Vertices of what? What does e represent?

Answer 2

I will assume you meant:

vertices are (7,0) and (-7,0) with e = 4/3

you must be talking about a horizontal hyperbola with an eccentricity of 4/3

for a hyperbola e > 1 and e = c/a
c/a = 4/3
so we could have c = 4, and a = 3
but since the vertex is (7,0) a must be 7 in our equation
so c/a = 4/3 = (28/3) / 7

c= 28/3 , a=7
in a hyperbola:
a^2 + b^2 = c^2
49 + b^2 = 784/9
b^ = 784/9 - 49
= 343/9

how about

x^2/49 - y^2/(343/9) = 1