Examples for

Coordinate Geometry

Coordinate geometry, or analytic geometry, is the study of geometry using an algebraic representation of a specified coordinate system to find and analyze relations between geometric figures. Wolfram|Alpha has knowledge about many geometric figures and is capable of determining the algebraic equations for them and computing geometric properties.
Lines

Compute the equation and draw the graph of a line.

Specify a line through two points:

line through (1,2) and (2,1)

Specify a line by slope and intercept:

line, slope=1/5, y-intercept=3
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Planes

Compute the equation and draw the graph of a plane in 3D.

Specify a plane through three points:

plane through (0, 1, 0), (5, 6, 7), and (6, 7, 8)
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Quadrants

Identify the quadrant in which a given 2D point lies.

Identify the quadrant that contains a given point:

What quadrant is (1,2) in?
is (-2, 2) in quadrant 4?
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Conic Sections

Identify and compute the properties of circles, ellipses, parabolas and hyperbolas.

Plot a conic section and identify its type:

x^2 - 2 y^2 = 1

Find a circle passing through three points:

circle through (0,0), (1,0), (0,1)

Compute properties of a parabola:

parabola with focus (3,4) and vertex (-4,5)
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Intercepts

Find the points of intersection for a geometric object with its coordinate axes.

Locate intercepts of a line or curve in the plane:

y-intercept of 3x-4y=5

Locate intercepts of a plane or surface:

z-intercepts of x/2 - y/3 + z/12 = 2
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