Hyperbolic paraboloid
Author: Joseph Lo

Curve at x = c_1

Curve at y = c_2

Level curve at z = c_3

Surface

Traces ∥ yz-plane

Traces ∥ xz-plane

Surface

$z = x^2-y^2$

f = Surface(s, t, s^(2) - t^(2), s, -1, 1, t, -1, 1)
c1 = 0 (slider from -1 to 1, step 0.05)
c2 = 0 (slider from -1 to 1, step 0.05)
yCurves = Sequence(CurveCartesian[t, i / 5, t^(2) - (i / 5)^(2), t, -1, 1], i, -5, 5)
xCurves = Sequence(CurveCartesian[i / 5, t, (i / 5)^(2) - t^(2), t, -1, 1], i, -5, 5)
c3 = 0.5 (slider from -1 to 1, step 0.05)
lCurveLimit: sqrt(abs(1 - abs(c3)))
lCurve1 = CurveCartesian(t, sqrt(abs(t^(2) - c3)), c3, t, (-lCurveLimit), lCurveLimit)
lCurve2 = CurveCartesian(t, (-sqrt(abs(t^(2) - c3))), c3, t, (-lCurveLimit), lCurveLimit)
lCurve3 = CurveCartesian(sqrt(abs(t^(2) + c3)), t, c3, t, (-lCurveLimit), lCurveLimit)
lCurve4 = CurveCartesian((-sqrt(abs(t^(2) + c3))), t, c3, t, (-lCurveLimit), lCurveLimit)
yCurve = CurveCartesian(t, c2, t^(2) - c2^(2), t, -1, 1)
xCurve = CurveCartesian(c1, t, c1^(2) - t^(2), t, -1, 1)
xPlane = Surface(c1, s, t, s, -1, 1, t, -1, 1)
yPlane = Surface(s, c2, t, s, -1, 1, t, -1, 1)
zPlane = Surface(s, t, c3, s, -1, 1, t, -1, 1)
xcheck = false
ycheck = false
zcheck = false
text3: "Level curve at z = " + c3 + ""
surfacecheck = true
xcurvescheck = false
ycurvescheck = false
text5_1: "$ " + (LaTeX[c3]) + " = x^2 - y^2$"
text5_2: "$ z = x^2 -( " + (LaTeX[c2]) + ")^2$"
P1: (c1, 0, 0)
P2: (0, c2, 0)
P3: (0, 0, c3)
text5: "\( z =( " + (LaTeX[c1]) + " )^2- y^2\)"
text1: "Traces along x = " + c1 + ""
text2: "Traces along y = " + c2 + ""
a = 0 (slider from 0 to 0, step 0.1)