Find the standard form of the equation of the hyperbola with the given characteristics.

Question

foci: (±4, 0) asymptotes: y= +/- 3x

Answer 1

we know c=4 and b/a = 3/1 so b = 3a
also in a standard hyperbola
a^2 + b^2 = c^2
a^2 + (9a^2) = 16
a^2 = 16/10 = 8/5

b^2 = 9a^2 = 72/5

standard form:
x^2/((8/5) - y^2/((72/5)) = 1

Answer 2

Thank you!!I was just having a hard time on finding out a and b but now I understand.