## ANALYTIC GEOMETRY FORMULAS

Analytic Geometry is a branch of algebra, an invention of Descartes and Fermat. It deals with modelling some geometrical objects, such as lines, points, curves, and so on. The study of analytic geometry is important as it gives the knowledge for the next level of mathematics.

## LINES IN TWO DIMENSIONS

Point direction form where (A, B) is the direction of the line and  P1 (X1,Y1) lies on the line.

satisfy 0 ≤ s ≤ 1 and 0 ≤ t ≤ 1

## CIRCLE

THEOREMES:

Chord theorem: The chord theorem states that if two chords, CD and EF intersect at G, then:

CD • DG = EG •FG

Tangent- secant theorem: if the tangent from an external point D intersects the circle at C and a secant from the external point D intersects the circle at G and E, then:

DC² = DG • DE

The secant-secant theorem: states that if two secants, DG & DE, cut the circle at H and F, respectively, then

DH •DG = DF • DE

Property of the tangent chord: The angle formed by a tangent and a chords is the equal to the subtended angle on the chord’s opposite side.

## PLANES IN THREE DIMENSIONS

Plane forms

Point direction form: where ( x1, y1, z1) lies in the plane, and the direction (a, b, c) is normal plane.

General form:

Ax + By + Cz + D = 0

where direction ( A, B,C) is the normal to the plane.

Intercept form: this plane passes through the points ( a, 0,0), (0,b,0), and (0,0,c)

Three point form: Angle between two planes:

The planes are parallel id and only if The planes are perpendicular if and only if Equation of a plane

The equation of a plane through P1 ( X1, Y1, Z1) and parallel to directions( a1, b1, c1) and ( a2, b2, c2) The equation of a plane through P1 (X1, Y1, Z1) and P2 (a2, b2, c2) and parallel to the direction (a, b, c), has equation. Distance

The distance of P1 (x1, y1, z1) from the plane Ax + By + Cz + D= 0 is Intersection

The intersection of two planes

A1y + B1y + C1z +D1 = 0,

A2x + B2y + C2z + D2 =0 