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Analytic Geometry 3D notes with problems and solution, Study notes of Mathematics

Mathematics

Formulas and examples related to analytic geometry, specifically distance, division of line segment, and common quadratic surfaces. It includes equations and models for spheres, ellipsoids, and planes, as well as methods for finding distances and points on lines and planes. The document also covers special cases and formulas for midpoint and equidistant points. The examples provided demonstrate how to apply these formulas to solve problems in analytic geometry.

Typology: Study notes

2022/2023

Available from 07/13/2023

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followtobulacanconcert 🇵🇭

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SoLtD (8D) ANALYTIC GEOMETRY J. Distance 8/4 2- paints Model: yi|e3 Pas Cage) \ ds P. Pe le Pa Oa5%, 22) mer by PT S = 2 SF amewer he [Gr mya (aH) 2e-?s) Example + 4) Find the distance from (3,72, 1) 46 €2;4,72) ah Solution = - af 2 is vse, AZ | Gea m4 C¥e-¥) 7 (22°29) lea] =a substdute waluct, ae \ yp ary? = OTE urerbotn 2-3)" ae» +@2 » —Z answer 2) Find the point en the Ine xe ye? that ic equidistant from the poink (30.5) and Ct) Solvton: L =3 “ery? aa 2 x, x) EHD 2 (2.9 wwer C4) A, > dz (30s) a? sels y* Cm 8944 CxO (ee) = Cx 4 Cx Ps ce 4® y solve for %, y ao hence, pe (2,22) -_? omsweor” J. Division oF LINE SEGMENT Pat (X%-#a) by RAP fo = (Xe, ¥e, Be) %e-% _ Yo- ¥! © a Ke-X We 4 Pre (Ky Hee 2) ZerBi gi Piteney, Formulas: * = Mo = 6 (X27) TK Zz OP Yo 2 C%2 “YF % Zet © Cz2-2:) ts * Special Cases — Midpoint, Y= Yo Me CX en, 7a pz) xm = Yz Cxet%) Ym = '/2 Cy An) 2m = /2 Cz242s)