DAY 12 FORMULA-CONICS

GENERAL EQUATIONS OF CONIC SECTIONS

HOW TO IDENTIFY IF THE EQUATION OF CONIC SECTIONS IS A PARABOLA

METHOD 1: DISCRIMINANT

METHOD 2: GENERAL EQUATION

HOW TO IDENTIFY IF THE EQUATION OF CONIC SECTIONS IS A CIRCLE

METHOD 1: DISCRIMINANT

METHOD 2: GENERAL EQUATION

HOW TO IDENTIFY IF THE EQUATION OF CONIC SECTIONS IS A ELLIPSE

METHOD 1: DISCRIMINANT

METHOD 2: GENERAL EQUATION

HOW TO IDENTIFY IF THE EQUATION OF CONIC SECTIONS IS A HYPERBOLA

METHOD 1: DISCRIMINANT

METHOD 2: GENERAL EQUATION

PARABOLA:

1

AT ORIGIN, FORMULA OF PARABOLA OPENING LEFT AND RIGHT

NOT ORIGIN, FORMULA OF PARABOLA OPENING LEFT AND RIGHT

AT ORIGIN, FORMULA OF PARABOLA OPENING DOWNWARD AND UPWARD

NOT ORIGIN, FORMULA OF PARABOLA OPENING DOWNWARD AND UPWARD

FORMULA OF LATUS RECTUM OF A PARABOLA

4P (ABSOLUTE VALUE)

FOCAL LENGTH OF PARABOLA

P

LATUS RECTUM AND SEMI-LATUS RECTUM OF PARABOLA

AXIS OF SYMMETRY OF PARABOLA

X=# OR Y=#

DIRECTRIX OF PARABOLA

X= -P OR Y= -P

CIRCLES:

1

FORMULA OF CIRCLE AT ORIGIN (0,0)

FORMULA OF CIRCLE AT NOT ORIGIN

CIRCLE CENTER-RADIUS FORM AKA STD. EQN.

ELLIPSE:

1

ELLIPSE FORMULA AT CENTER (0,0)

ELLIPSE FORMULA AT NOT CENTER

ARBITRARY CONSTANT IN ELLIPSE FORMULA

MAJOR AXIS FORMULA

2a

MINOR AXIS FORMULA

2b

ELLIPSE B-SQUARED FORMULA OR RELATIONSHIP OF A,B,C (RELATIONSHIP OF SEMI-MAJOR, SEMI-MINOR, AND FOCI)

B² = A² - C²

LATUS RECTUM OF AN ELLIPSE (SAME WITH HYPERBOLA)

SEMI-MAJOR AXIS FORMULA

= A

SEMI-MINOR AXIS FORMULA

= B

AREA OF ELLIPSE

DIRECTRIX OF AN ELLIPSE

HYPERBOLA:

1

STANDARD FORM OF HYPERBOLA

FORMULA OF HYPERBOLA AT ORIGIN (0,0)

FORMULA OF HYPERBOLA AT NOT ORIGIN

HYPERBOLA. B-SQUARED FORMULA OR RELATIONSHIP OF A, B, C

(RELATIONSHIP OF SEM-TRANSVERSE, SEMI-CONJUGATE, FOCI)

B² = C² - A²

CONSTANT FORMULA OF HYPERBOLA

2a=

TRANSVERSE AXIS FORMULA

SEMI-TRANSVERSE AXIS FORMULA

=A

CONJUGATE AXIS FORMULA

SEMI-CONJUGATE AXIS FORMULA

=B

ASYMPTOTE FORMULA AT ORIGIN

ASYMPTOTE FORMULA AT NOT ORIGIN

EQUATE THE STD FORM OF HYPERBOLA TO ZERO

DE-FACTOR THE EQN USING DIFFERENCE OF TWO SQUARES

SOLVE FOR Y

ECCENTRICITY OF HYPERBOLA FORMULA (2)

ECCENTRICITY OF HYPERBOLA FORMULA (additional)

LATUS RECTUM OF HYPERBOLA