How this calculation works
Recover the foci and slopes of the asymptotes of a horizontal hyperbola centred at the origin.
THE FORMULA
For x²/a²−y²/b²=1, c=hypot(a,b) and slopes are ±b/aA worked example
With a=3 and b=4 the focal offset is 5 and the slopes are ±4/3.
Good to know
The transverse axis is horizontal.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Recover the foci and slopes of the asymptotes of a horizontal hyperbola centred at the origin.
The primary result is labeled “Focal offset”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The transverse axis is horizontal.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
With a=3 and b=4 the focal offset is 5 and the slopes are ±4/3.
Which rule does this calculator apply?
For x²/a²−y²/b²=1, c=hypot(a,b) and slopes are ±b/a