# Analytic Geometry

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Reseña del editor:

analytic geometry, points line segments and lines in coordinate plane, Cartesian coordinate, distance formula length of line segment, midpoint formula, dividing line segment in given ratio, area of triangle, coordinates of centroid of triangle, equation of line, definition of slope of line, slope-intercept form of line, intercept form of equation of line, lines parallel to axes, horizontal and vertical lines, point-slope form of line, translation of line in direction of coordinate axes, two point form of equation of line, parallel and perpendicular lines, angle between two lines, general or implicit form of equation of line, pencil or sheaf of lines, Hessian normal form of equation of line, angle bisector of two lines, distance between point and line, parametric equations of line, parametric curves have direction of motion, points, line segments and lines examples, conic sections, circle, general equation of circle with center S(p, q), translated circle, equation of circle example, equation of circle at origin, circle through three points, equation of circle through three points example, circle and line, line circle intersection, circle and line examples, equation of tangent at point of circle with center at origin, equation of tangent at point of translated circle, equation of tangent at point of circle examples, condition of tangency, condition for line to be tangent to circle, condition for line to be tangent to translated circle, tangents to circle from point outside the circle, angle between line and circle, radical line or radical axis, pole and polar, angle between two circles, ellipse, definition of ellipse, construction of ellipse, equation of ellipse, standard equation of ellipse, major axis of ellipse, minor axis of ellipse, vertices of ellipse, focal parameter of ellipse, latus rectum, parametric equation of ellipse, equation of translated ellipse, ellipse and line, condition of tangency for ellipse, equation of tangent at point on ellipse, construction of tangent at point on ellipse, angle between focal radii at point on ellipse, tangents to ellipse from point outside ellipse, use of tangency condition, construction of tangents from point outside ellipse, polar and pole of ellipse, equation of polar of ellipse of given point, definition and construction of hyperbola, equation of hyperbola, properties of hyperbola, equilateral or rectangular hyperbola, translated hyperbola, equation of hyperbola in vertex form, parametric equation of hyperbola, examples of hyperbola, equilateral or rectangular hyperbola with coordinate axes as its asymptote, hyperbola and line, hyperbola and line relationships, condition for line to be tangent to hyperbola, tangency condition for hyperbola, equation of tangent at point on hyperbola, polar and pole of hyperbola, construction of tangent at point on hyperbola, construction of tangent from point outside hyperbola, properties of hyperbola, area of triangle tangent at point on hyperbola forms with asymptotes, equation of equilateral or rectangular hyperbola with coordinate axes as its asymptotes, hyperbola and line examples, parabola, definition of parabola, construction of parabola, vertex form of equation of parabola, transformations of equations of parabola, equation of translated parabola, standard form of equation of parabola, parabola whose axis of symmetry is parallel to y-axis, equation of parabola written in general form, parametric equation of parabola, parabola examples, parabola and line, common points of line and parabola, condition for line to be tangent to parabola, tangency condition for parabola, equation of tangent and normal at point on parabola, properties of parabola, polar of parabola, construction of tangent at point on parabola, construction of tangents from point exterior to parabola, parabola and line examples, conics family of similarly shaped curves, properties of conics, Dandelin spheres proof of conic sections focal properties,

Biografía del autor:

Vladimir Serdarushich received MSc degree from Zagreb University, Croatia. He has taught mathematics and computer programming at high school for more than 30 years. He is the author of high school level mathematics textbooks relating to algebra, precalculus and calculus, and textbooks in computer programming.

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