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,