How this calculation works
Locate the focus and directrix of a vertical parabola given its vertex and signed focal parameter.
THE FORMULA
(x−h)²=4p(y−k) gives focus (h,k+p) and directrix y=k−pA worked example
Vertex (1,2) and p=3 give focus (1,5) and directrix y=−1.
Good to know
Negative p opens downward. Zero p is degenerate.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Locate the focus and directrix of a vertical parabola given its vertex and signed focal parameter.
The primary result is labeled “Focus y”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Negative p opens downward. Zero p is degenerate.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Vertex (1,2) and p=3 give focus (1,5) and directrix y=−1.
Which rule does this calculator apply?
(x−h)²=4p(y−k) gives focus (h,k+p) and directrix y=k−p