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Geometric Curves

YGK These Geometric Curves

QuestionAnswer
Distance from circle center to circumference Radius
Ratio of circle circumference to diameter Pi (π)
Wedge shape bounded by two radii and an arc Sector
Line segment joining two points on a circumference Chord
Shape where a circle passes through all vertices Cyclic shape
Cartesian equation of a circle (x-h)^2+(y-k)^2=r^2
Curves formed by a plane intersecting a double cone Conic sections
Ratio of distance to focus vs. distance to directrix Eccentricity
Eccentricity of a circle Zero
Conic section resembling an oval with eccentricity < 1 Ellipse
Line segments on an ellipse's axes of symmetry Major and minor axes
Law stating planetary orbits are ellipses Kepler’s first law
Open conic section with eccentricity of 1 Parabola
Path of a projectile in a constant gravitational field Parabolic arc
Conic section with eccentricity > 1 and two branches Hyperbola
Straight lines that a hyperbola's branches approach Asymptotes
Curve traced by a point on a rolling circle Cycloid
Problem of the fastest descent curve Brachistochrone problem
Problem where descent time is independent of starting position Tautochrone problem
Shape of a hanging chain Catenary
Function used to graph a catenary Hyperbolic cosine (cosh)
Bell-shaped curve \(y=1/(1+x^{2})\) Witch of Agnesi
First woman math professor who popularized the "Witch" curve Maria Agnesi
Spiral where radius is a linear function of the angle Archimedean spiral
Spiral where radius is an exponential function of the angle Logarithmic spiral
Heart-shaped curve from a circle rolling around another circle Cardioid
"Snail" curve defined by Etienne Pascal Limaçon
Figure-8 shaped curves Lemniscates
Symbol represented by a lemniscate Infinity
Created by: divyap
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