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Ellipse: Quiz


Question 1: Such elliptical gears may be used in mechanical equipment to produce variable angular speed or ________ from a constant rotation of the driving axle.
ForceTorqueEnergyAngular momentum

Question 2: Each focus F of the ellipse is associated to a line D perpendicular to the major axis (the ________) such that the distance from any point on the ellipse to F is a constant fraction of its distance from D.
Projective geometryParabolaHyperbolaConic section

Question 3: In geometry, an ellipse (from Greek ἔλλειψις elleipsis, a "falling short") is a plane curve that results from the intersection of a ________ by a plane in a way that produces a closed curve.
ConeCracker Creek ConeSidas ConeCone Glacier Volcano

Question 4: More generally, the ________ of a portion of the circumference, as a function of the angle subtended, is given by an incomplete elliptic integral.
Arc lengthCurvePiCalculus

Question 5: By ________, an ellipse can be defined also as the envelope of all lines that connect corresponding points of two lines which are related by a projective map.
Duality (projective geometry)Projective planeProjective spaceIncidence (geometry)

Question 6: As the eccentricity tends to 1, the ellipse gets a more elongated shape and tends either towards a line segment (see below) or a ________, and the ratio a/b tends to infinity.
ParabolaHyperbolaArchimedesConic section

Question 7: In analytic geometry, the ellipse is defined as the set of points (X,Y) of the ________ that satisfy the implicit equation
Cylindrical coordinate systemSpherical coordinate systemCartesian coordinate systemParabolic coordinates

Question 8: Alternatively, they can be connected by a link chain or ________.
Four-stroke engineEngine tuningTiming beltBelt (mechanical)

Question 9: Ellipses also arise as images of a ________ under parallel projection and some cases of perspective projection.
Conic sectionPiGeometryCircle

Question 10: The image of an ellipse by any ________ is an ellipse, and so is the image of an ellipse by any projective map M such that the line M−1(Ω) does not touch or cross the ellipse.
Affine geometryAffine transformationMatrix (mathematics)Eigenvalue, eigenvector and eigenspace

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