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Mastering Parabola Equations: A Comprehensive Guide

Dive deep into the world of parabolas with this comprehensive guide covering vertex, focal chord, axis, and more. Learn how to solve equations, find tangents and normals, and unlock the secrets of this fascinating curve.

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Mastering Parabola Equations: A Comprehensive Guide

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  1. Terms Equation of parabola yy = 4ax Vertex Equation of Chord y(y1+y2)=4ax+y1y2 Axis y2-->y1 Focal chord Focus Latus rectum Parabola Tangent at P y1y = 2a(x+x1) Normal Normal at P y - y1 = -y1/2a(x - x1) Tangents Tangent at t y = x/t+at k = h/t + t and solve t Condition for tangency c = a/m Normal at t y + tx = 2at + at^3 Tangent from P(h, k) k = mh + a/m and solve m. Equation of tangent with m y = mx + a/m

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