Simple Curve Calculator

Formulas

Tip: Leave unused fields blank. Units are assumed arbitrary. Results rounded to 6 decimals.

Brief Formulas

Circle

Center (h,k), radius r

  • Eqn: (x−h)2 + (y−k)2 = r2
  • Circumference: C = 2πr
  • Area: A = πr2

Parabola

y = a(x−h)2 + k

  • Vertex: (h,k)
  • Opens: a > 0 up, a < 0 down
  • Focal length: p = 1/(4a)
  • Focus: (h, k + p)
  • Directrix: y = k − p

Ellipse

(x−h)2/a2 + (y−k)2/b2 = 1

  • c = √(a2 − b2) (assume a ≥ b)
  • Eccentricity: e = c/a
  • Area: A = πab
  • Foci: (h±c, k)

Hyperbola

(x−h)2/a2 − (y−k)2/b2 = 1

  • c = √(a2 + b2)
  • Eccentricity: e = c/a
  • Asymptotes: y − k = ±(b/a)(x − h)
  • Foci: (h±c, k)

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