Skill — Geometria analitica.
Featured in chapters
12·13·16·17·18·19·20·21·22·24·28·37·42·44
Linked atoms
132 linked atoms.
12 La parabola
- Line tangent to the parabola
- Line–parabola intersections
- Rectangle of maximum area in a semicircle
- Two forms for finding the equation
13 Radicali ed equazioni irrazionali
16 Circonferenza
- Distance of a point from a line
- Perpendicular bisector of a segment in coordinates
- Point on a parabola at a given distance
17 Disequazioni irrazionali
- Application — lines at an assigned distance
- Distances in analytic geometry
- Example — distance in a pencil of lines
18 Fasci di rette
- Complete study of a pencil
- Example — Fixed distance
- Example — Passing through a point
- Example — Secant, tangent, external
- Example — Tangency to a parabola
- General method for pencil problems
- Proper and improper pencils compared
- The improper pencil
- The pencil with two generators
- The proper pencil
- The single-parameter notation
- The strategy for determining the parameter
19 Luoghi geometrici nel piano cartesiano
- A unifying definition of the conics
- Bisectors of two given lines
- Bisectors of two lines
- Formulae for focus, vertex and directrix
- Locus
- Parabola from focus and directrix
- Parabola from focus and directrix
- Perpendicular bisector of a given segment
- Perpendicular bisector of a segment
- The bisector as a locus
- The parabola as a locus
- The perpendicular bisector as a locus
- Why the locus is a line
20 Circonferenza nel piano cartesiano
- Centre, radius and position of a point
- Circle tangent to two lines: the angle-bisector trick
- Definition of a circle
- Equation from centre and radius
- Example — intersection of two circles
- Example — tangents with the delta method
- Example — tangents with the distance method
- From the definition to the equation
- How to determine a circle
- How to intersect two circles
- Implicit and explicit form
- Radical axis and intersections
- Relative positions of a line and a circle
- Tangent at a point of the circle
- Tangents with the distance method
- The delta method and the distance method
- The method of tangents from a point
- The radical axis
- When an equation is a circle
21 Ellisse
- Canonical equation
- Elements of 9x²+4y²=36
- Elements of the ellipse
- Ellipse given the foci and a point
- Example - determining the elements
- Proof of the canonical equation
- Recognising a translated ellipse
- Recognising an ellipse
- Translated ellipses
22 Iperbole e funzione omografica
- Asymptotes and centre of symmetry
- Canonical equation
- Elements of a hyperbola
- Example — studying a homographic function
- Foci, vertices, asymptotes and eccentricity
- Recognising a conic
- Rectangular hyperbola referred to its asymptotes
- Rectangular hyperbola xy=6
- Study of a homographic function
- Translated and non-rectangular hyperbolas
24 Trasformazioni nel piano cartesiano
- Composizione di trasformazioni
- Dilatazioni e omotetie
- Ellipses as dilated circles
- Isometrie
- Rotazioni
- Simmetrie assiali
- Simmetrie centrali
- Square root reflected across the y-axis
- Symmetric point with respect to a line
- Transformation from circle to ellipse
- Translated parabola
- Traslazioni
28 Circonferenza goniometrica e funzioni sin, cos, tan
37 Geometria analitica nello spazio
- Cartesian coordinates in space
- Cartesian form of the line
- Distance between two skew lines
- Distance, midpoint and centroid
- Equation of the plane
- Equation of the sphere
- Example - distance between two points
- Example - skew lines
- Improper pencil
- Improper pencil parallel to a plane
- Line-plane and plane-plane distances
- Parallel and perpendicular component
- Parallel vectors
- Parametric form of the line
- Parametric-Cartesian conversion
- Pencil of planes
- Plane through a point with given normal
- Plane through three points
- Plane through three points
- Point-line distance
- Point-line distance
- Point-plane distance
- Proper pencil
- Proper pencil through a line
- Radius of the section
- Relative position of two lines
- Relative positions of line and plane and angles
- Scalar product
- Sphere and plane
- Sphere centre radius and tangent plane
- Sphere-plane position
- Tangent plane to the sphere
- Thales in space
- The four cases
- Three planes and a common point
- Unit vector
- Vector in space
- Vector product
- Vector, magnitude and midpoint