Question

What is the equation of a hyperbola with a = 1 and c = 9? Assume that the transverse axis is horizontal.

Answer 1

Answer:

Step-by-step explanation:

The general formula for a horizontal hyperbola :

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

Given: a = 1 we know a² = 1 ,and that c = 9 so we know c² = 9² = 81

We also know that the relation between a, b, c for a hyperbola is c²= a²+b²

c²= a²+b², substitute what we know

81 = 1 +b², subtract 1 from both sides of the equation

80 = b²

The equation of our hyperbola is:

$\frac{x^{2} }{1 } -\frac{y^{2} }{80 } =1$  or  $x^{2} -\frac{y^{2} }{80} =1$