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General Equation for Parabola - Proof

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#algebra-precalculus #geometry #analytic-geometry #conic-sections
77
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Finding the eccentricity of the conic $(3x + 9)^2 + (3y – 12)^2 – (2x – y)^2 = 6y – 12x + 9$

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#conic-sections
558
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Why does the focus-directrix definition of the parabola work?

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#conic-sections
1k
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How to parametrize a shifted and tilted ellipse from its quadratic equation

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#conic-sections #parametrization
292
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Find the envelope of ellipses defined by a difficult function

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#manifolds #conic-sections #envelope
41
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Can we say $(x_1 , y_1)$ will be outside the parabola iff $A{x_1}^2 + 2H{x_1}{y_1} +B{y_1}^2+ 2G{x_1} +2 F{y_1} +C > 0$?

Published on
#conic-sections
413
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How to compute the diameter of a truncated cone?

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#geometry #euclidean-geometry #conic-sections
57
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What is the condition of the point $(x_1 , y_1)$ being outside the parabola $Ax^2 + 2Hxy +By^2 + 2Gx +2 Fy +C=0$ $(H^2 = AB)$?

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#conic-sections
37
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Classify a conic on a plane

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#analytic-geometry #conic-sections
50
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Get ellipsoid information from "it's matrix"

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#conic-sections
250
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Calculating major axis of conical section

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#conic-sections
49
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Flow along hyperbolas

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#dynamical-systems #conic-sections #integer-lattices
699
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A parabola is an ellipse with one focus at infinity

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#conic-sections
147
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Problem related to incident and reflected rays in an ellipse

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#geometry #conic-sections #tangent-line
46
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Query regarding $(x^2 + αy^2 + β) (y^2 – xy – 2x^2) = 0$

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#conic-sections

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