The Computer Graphics Companion Online Edition Damian Scattergood 1999-2001
Index Home	Download HelpFile

CO-ORDINATE GEOMETRY

CO-ORDINATE GEOMETRY - LINE

Slope of

· Parallel Lines:

· Perpendicular Lines:

· General Equation of the line Þ
If it cuts then it becomes

· The Length of a line

· Angles Between Lines =

· The Equations of the line passing through the point of intersection

of is of the form

is found when some other condition is known.

· Bisectors

CO-ORDINATE GEOMETRY - CIRCLE

· The General Equation of a circle

· Equation of circle with centre

· For the General Circle the equation becomes

· is the equation of the Tangent to the circle

· Length of Tangent from to Circle =

· two intersecting circles, then for a given real value of

is the equation of a circle containing the points of intersection of both

NOTE:
If is a linear equation. It is the equation of the line through the point of intersection of the two circles. This is called the

Radical Axis and contains the common chord.

· Orthogonal if...

· If are the equations of an intersecting Circle and Line then

is the equation of a circle containing the points of intersection of S = 0 and L = 0.

CO-ORDINATE GEOMETRY - Ellipse

·

·

CO-ORDINATE GEOMETRY - Hyperbola

·

·

CO-ORDINATE GEOMETRY - PARABOLA

· Definition:
A Parabola is the locus of the points each of which is equidistant from a given point S and a given line D.

The given point S is called the focus. The given line D is called the directrix.

· Equation:

· Latus Rectum

· is the equation of a Parabola having

NOTE:
is the axis of the parabola (equation).

· Parametric Equation

are the parametric equations of the parabola

If is a focal chord of the parabola then the product of

the parameters is

· is the equations of the tangent to the parabola

at the point

NOTE:
The equations of the tangent is obtained by writing

and

· The line is a tangent to the parabola

NOTE:

· Diameter of a Parabola

CO-ORDINATE GEOMETRY - TRIANGLE

· The Area of a Triangle.

For the given Triangle with Vertices at the area is

given by the equation

For the given Triangle with Vertices at the area is

given by the equation

However it is worth noting that for speed of calculation it is more efficient to translate a triangle to (0,0) and
using the simpler equation.

GRAVITY

Newtons Law Of Gravity:

"The force between two bodies in the universe is proportional to the
product of the masses and is inversely proportional to the square of their distance apart"

where (G) = universal constant of gravitation

G is the same everywhere.

g (planetary g) varies.

For a planet m = Weight, r = Radius and G = Gravity.

SURFACES AND CURVES

Other useful equations: