FORMULA ANALYTIC GEO. DAY 12

INTRO TO CONIC SECTIONS

GENERAL EQUATIONS OF CONIC SECTIONS

FROM GENERAL EQN OF CONICS. HOW TO IDENTIFY WHAT TYPE OF CONIC (2)

A & C METHOD

DISCRIMINANT METHOD

IDENTIFYING PARABOLA FROM GEN EQN OF CONIC USING A&C METHOD

IDENTIFYING ELLIPSE FROM GEN EQN OF CONIC USING A&C METHOD

IDENTIFYING CIRCLE FROM GEN EQN OF CONIC USING A&C METHOD

IDENTIFYING HYPERBOLA FROM GEN EQN OF CONIC USING A&C METHOD

IDENTIFYING PARABOLA FROM GEN EQN OF CONIC USING DISCRIMINANT METHOD

IDENTIFYING HYPERBOLA FROM GEN EQN OF CONIC USING DISCRIMINANT METHOD

IDENTIFYING CIRCLE FROM GEN EQN OF CONIC USING DISCRIMINANT METHOD

IDENTIFYING ELLIPSE FROM GEN EQN OF CONIC USING DISCRIMINANT METHOD

CIRCLES

STD EQN OF CIRCLES

CENTER RADIUS FORM OF CIRCLE

PARABOLA

GENERAL EQUATIONS OF PARABOLA

AXIS PARALLEL TO THE Y-AXIS

GENERAL EQUATIONS OF PARABOLA

AXIS PARALLEL TO THE X-AXIS

STANDARD EQUATIONS OF PARABOLA

VERTEX AT (0,0)

AXIS ALONG X-AXIS

OPENS TO RIGHT & OPENS TO LEFT

STANDARD EQUATIONS OF PARABOLA

VERTEX AT (0,0)

AXIS ALONG Y-AXIS

OPENS UPWARD & OPENS DOWNWARD

STANDARD EQUATIONS OF PARABOLA

VERTEX AT (h,k)

AXIS ALONG X-AXIS

OPENS TO RIGHT & OPENS TO LEFT

STANDARD EQUATIONS OF PARABOLA

VERTEX AT (h,k)

AXIS ALONG Y-AXIS

OPENS UPWARD & OPENS DOWNWARD

ECCENTRICITY OF PARABOLA

LATUS RECTUM OF PARABOLA

a=p

p = is the distance from directrix to vertex and vertex to focus AKA FOCAL LENGTH

ELLIPSE

GENERAL EQUATION OF ELLIPSE

STANDARDS EQUATIONS OF ELLIPSE

C (0,0)

WHERE

MAJOR AXIS IS HORIZONTAL &

MAJOR AXIS IS VERTICAL

STANDARDS EQUATIONS OF ELLIPSE

C (h,k)

WHERE

MAJOR AXIS IS HORIZONTAL &

MAJOR AXIS IS VERTICAL

ECCENTRICITY OF ELLIPSE

RELATIONSHIP OF A,B,C OF ELLIPSE

CONSTANT FORMULA

2a = #

MAJOR AXIS FORMULA

=2a

MINOR AXIS FORMULA

=2b

LATUS RECTUM OF ELLIPSE

HYPERBOLA

GENERAL EQUATIONS OF HYPERBOLA

LENGTH OF TRANSVERSE AXIS

LENGTH OF CONJUGATE AXIS

STANDARD EQUATIONS OF HYPERBOLA

AT C(0,0)

TRANSVERSE AXIS HORIZONTAL & VERTICAL

STANDARD EQUATIONS OF HYPERBOLA

AT C(h,k)

TRANSVERSE AXIS HORIZONTAL & VERTICAL

ECCENTRICITY OF HYPERBOLA

RELATIONSHIP OF A,B,C OF HYPERBOLA

LATUS RECTUM

ASSYMPTOTE FORMULA OF HYPERBOLA AT ORIGIN FOR HORIZONTAL AND VERTICAL TRANSVERSE AXIS

HORIZONTAL VERTICAL

ASSYMPTOTE FORMULA OF HYPERBOLA AT (h,k) FOR HORIZONTAL AND VERTICAL TRANSVERSE AXIS

HORIZONTAL VERTICAL

TRANSVERSE AXIS FORMULA

=2a

SEMI-TRANSVERSE AXIS FORMULA

=a

CONJUGATE AXIS FORMULA

=2b

SEMI-CONJUGATE AXIS FORMULA

=b

SPHERE

STD EQN OF SPHERE AT ORIGIN

STD EQN OF SPHERE AT (h,k)

POLAR COORDINATES

ADTLS:

ECCENTRICITY OF CONIC SECTIONS