Parabola Tangent-Projection Locus Explorer

Parabola Moving point B Tangent at B Fixed point C Projection D Full locus of D

Geometry and motion

Parabola coefficient a

Fixed point C: x

Fixed point C: y

Moving parameter x

Swing speed

Locus resolution

The x slider is constrained to b5[-5,5]. Animation follows a reflected linear motion, so B travels from −5 to +5, reverses smoothly, then returns to −5.

Current quantities

Moving point B—

Projection D—

Tangent slope—

Projection distance CD—

Locus x range—

Parabola: y = ax²

At B = (u, au²), tangent:
y = 2au·x − au²

For C = (cₓ,cᵧ), the perpendicular foot is:
D = C + q(−m, 1),
q = (m cₓ − cᵧ − au²)/(m²+1),
where m = 2au.

Animation domain: u ∈ [−5, +5].