PRECAL LESSON 1-4: 1ST QUARTERLY EXAMINATION

CONIC SECTIONS

SER OF CURVES FORMED DIVING OR CUTTING A RIGHT CIRCULAR CONE OF TWO NAPPLE WITH A PLANE

CONIC SECTIONS

THE PLANE INTERSECTS THE TWO INVERTED RIGHT CIRCULAR CONES AT ANY POINT EXCEPT ITS VERTEX

CONIC SECTIONS

DIFFERENT CURVES FORMED WHEN A PLANE CUTS THROUGH A CONE. THEY INCLUDE THE CIRCLE, ELLIPSE, PARABOLA, AND HYPERBOLA

CIRCLE, PARABOLA, ELLIPSE, HYPERBOLA

ENUMERATE THE TYPES OF CONIC SECTIONS

CIRCLE

A=C

PARABOLA

A=0 OR C=0 (y² or x²)

ELLIPSE

A≠C (SAME SIGN)

HYPERBOLA

A≠C (DIFFERENT SIGN)

CIRCLE

CONSIST OF POINTS ON THE PLANE EQUIDISTANT FROM A FIXED POINT CALLED THE CENTER

CIRCLE

THE DISTANCE FROM THE CENTER TO ANY POINT ON THE CIRCLE IS CONSTANT AND IS CALLED THE RADIUS OF A CIRCLE

CIRCLE

ALWAYS EQUALS TO r²

STANDARD FORM

(x - h)² + (y - k)² = r²

QUADRATIC TERM

Ax² and Cy²

LINEAR TERM

Dx and Ey

ANY CONSTANT

F

GENEREAL EQUATION

Ax² + Cy² + Dx + Ey + F = 0

DISTANCE FORMULA

DISCRIMINANT FORMULA

b² - 4ac

PARABOLA

SECOND COMMONLY KNOWN CONIC SECTION

PARABOLA

DEFINED AS A CURVE THAT HAS POINTS WHICH ARE EQUIDISTANT

VERTEX, DIRECTRIX LINE, FOCUS, FOCAL DISTANCE, LATUS RECTUM, AXIS OF THE PARABOLA, ECCENTRICITY

7 PARTS OF THE PARABOLA

VERTEX

MAIN POINT OF THE PARABOLA

VERTEX

LIES AT THE MIDDLE PORTION OF THE CURVE

VERTEX

MIDPOINT OF THE FIXED POINT OF THE CURVE AND THE GIVEN LINE

VERTEX

MIDDLE OF FOCUS AND DIRECTRIX

DIRECTRIX LINE

A LINE WHICH IS OUTSIDE AND PARALLEL TO THE PARABOLA CURVE

DIRECTRIX LINE

GIVEN LINE

FOCUS

LOCATED INSIDE THE CURVE

FOCUS

FIXED POINT OF THE PARABOLA

FOCAL DISTANCE

LENGTH OF SPACE FROM THE FOCUS TO THE VERTEX

FOCAL DISTANCE

DISTANCE BETWEEN THE DIRECTRIX LINE AND THE VERTEX

LATUS RECTUM

CHORD THAT IS PARALLEL TO THE DIRECTRIX LINE AND INTERSECTING THE PARABOLA AT THE POINT OF THE FOCUS

LATUS RECTUM

END POINTS ARE DEFINED AS R1 AND R2

LATUS RECTUM

LIES AT THE FOCUS

LATUS RECTUM

X4 OF THE FOCUAL DISTANCE

AXIS OF THE PARABOLA

AKA AXIS OF SYMMETRY

AXIS OF THE PARABOLA

LINE THAT DIVIDES IN 2 EQUAL PARTS

ECCENTRICITY

ALWAYS EQUALS TO 1

ELLIPSE

THE SHAPE OF THE _______ IS AN ELONGATED SPHERE SIMILAR TO THE SHAPE OF THE ORBIT OF THE EARTH IN THE SOLAR SYSTEM

ELLIPSE

FORMED BY A LOCUS OF POINTS WHOSE SUM OF THE DISTANCE FROM THE TWO FIXED POINTS IS CONSTANT

ELLIPSE

FORMULA IS 2a

CENTER, VERTICES, FOCI, DIRECTRIX LINE, MINOR AXIS, MAJOR AXIS, FOCAL DISTANCE, LATERA RECTA, ECCENTRICITY

WHAT ARE THE 9 PARTS OF AN ELLIPSE

CENTER

MIDPOINT INSIDE OF THE ELLIPSE CURVE AND DETONATED BY THE SYMBOL C

VERTICES

MAIN POINTS OF THE CURVE EXPRESSED BY THE SYMBOL V

FOCI

PLURAL FORM OF FOCUS

FOCI

FIXED POINTS OF THE ELLIPSE

FOCI

BETWEEN THE CENTER AND THE VERTICES

FOCI

SYMBOLS F1 AND F2

FOCI

FIXED POINT OF AN ELLIPSE

DIRECTRIX LINE

ALSO CALLED DIRECTRICES

DIRECTRIX LINE

OUTSIDE OF THE ELLIPSE

MINOR AXIS

DIVIDES THE CURVE INTO TWO SYMMETRICAL PARTS

MINOR AXIS

END POINTS OF THIS AXIS ARE CALLED INTERCEPTS

MINOR AXIS

LENGTH OF THE MINOR AXIS IS 2b

PRINCIPAL AXIS / MAJOR AXIS

ANOTHER SYMMETRICAL AXIS IN THE ELLIPSE BUT ALWAYS LONGER IN LENGTH COMPARED TO MINOR AXIS

PRINCIPAL AXIS / MAJOR AXIS

END POINTS OF THE ____________ ARE THE VERTICES

VERTICES

WHAT ARE THE END POINTS OF THE MAJOR AXIS

INTERCEPTS

WHAT ARE THE END POINTS OF A MINOR AXIS

PRINCIPAL AXIS / MAJOR AXIS

LENGTH OF THE MAJOR AXIS IS 2a

FOCAL DISTANCE

DISTANCE BETWEEN ONE OF THE FOCUS TO THE CENTER

FOCAL DISTANCE

SYMBOL c

LATERA RECTA

PLURAL FORM OF THE LATUS RECTUM

LATERA RECTA

LENGTH OF THE _________ IS 2b²/a

LATERA RECTA

SHOWS HOW WIDE OR NARROW AN ELLIPSE IS

ECCENTRICITY

RATIO OF THE DISTANCES FROM THE FIXED POINT (FOCI) TO THE POINT P AND POINT P TO THE DIRECTRIX LINE

ECCENTRICITY

VALUE CAN BE OBTAINED FROM THE FORMULA OF c/a

ECCENTRICITY

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