How do you find "b" in the equation of a hyperbola?

Question

Just for reference the equation is x^2/a^2 - y^2/b^2 = 1 or y^2/a^2 - x^2/b^2 = 1.

I no longer have my old trigonometry book and as of now I can't remember how to do it.

Yes...I thought it was b*2 = c*2 - a*2 at first but...

Answer 1

The quantity a is the distance from the origin to a vertex of the hyperbola. Let c be the distance from the origin to a focus of the hyperbola. Then b is given by the expression

b*2 = c*2 - a*2

Answer 2

Two equations given:
(1) y² / b² = 1
→ y² = b²
→ y = b eq.1

(2) y² / a² - x² / b² = 1
y² / a² = 1 + x² / b²
y² / a² = (b² + x²) / b² (invert)
a² / y² = b² / b² + x²
But y = b from equation one.
a² / y² = b² / y² + x²
b² = (a² / y²)(y² + x²)
b² = (a²)(1 / y²)( y² + x²)
b² = (a²)(1 + x² /y²)
b = √[(a²)(1 + x² /y²)]

Answer 3

x²/a² - y²/b² = 1
also
e = √(1+ b²/a²)

Answer 4

You have some way to determine a value for x, y and a. Substitute those values and solve for b.

Answer 5

x^2/a^2 - y^2/b^2 = 1
rewrite above equation into :
y^2/b^2 = x^2/a^2 - 1
y^2/b^2 = (x^2 - a^2)/a^2
b^2 = (a.y)^2 / (x^2 - a^2)
so we can write b as
b = a.y / sqrt ((x-a)(X+a))