how do i write an equation for a hyperbola with the give information, vertices (-4,0) (4,0) conjugate axis length of 8
The transverse axis is the line segment between the vertices (-4,0) and
(4,0) which is 8 units long. Its midpoint is the origin. The transverse
axis is horizontal so the equation is of the form:
- = 1
where a = one-half the transverse axis, which is half of 8 or 4, and
where b = one-half the conjugate axis, which is half of 8 or 4, so
a and b are both 4, so the equation is
- = 1
- = 1
That's the standard form, or you can clear of fractions and get
x² - y² = 16
Edwin