College Algebra 9th txtbk

Circle
(x h) 2 (y k) 2 r 2
x 2 y 2 r 2
Parabola
Center at (h, k); radius r
Center at (0, 0); radius r
Hyperbola
x 2
a y2
2 b 1 Foci: F¿(c, 0), F(c, 0); 2 c2 a 2 b 2
y 2
a 2 x2
b 2 1 Foci: F¿(0, c), F(0, c); c2 a 2 b 2
y 2 4ax,
x 2 4ay,
a 0, opens right; a 0, opens left
Focus: (a, 0); Directrix: x a
a 0, opens up; a 0, opens down
Focus: (0, a); Directrix: y a
Translation Formulas
x x¿ h, y y¿ k; x¿ x h, y¿ y k
New origin (h, k)
Ellipse
x 2
a y2
2 b 1, a 7 b 7 0
2 Foci: F¿(c, 0), F(c, 0); c 2 a 2 b 2
x 2
b y2
2 a 1, a 7 b 7 0
2 Foci: F¿(0, c), F(0, c); c 2 a 2 b 2
Metric Units
Standard Units of Metric Measure
Important Prefixes
Meter (m): length (approximately 3.28 ft) kilo ( 1,000) deci
Liter (L): volume (approximately 1.06 ft) hecto ( 100) centi
Gram (g): weight (approximately 0.035 oz) deka ( 10) milli (
( 1
10)
( 1
100)
1
1,000)
Abbreviations
Length Volume Weight
m meter dm decimeter L liter dL deciliter g gram dg decigram
km kilometer cm centimeter kL kiloliter cL centiliter kg kilogram cg centigram
hm hectometer mm millimeter hL hectoliter mL milliliter hg hectogram mg milligram
dam dekameter daL dekaliter dag dekagram
English-Metric Conversion
Length Volume (U.S.) Weight Length Volume (U.S.) Weight
1 in 2.540 cm 1 pt 0.4732 L 1 oz 28.35 g 1 cm 0.3937 in 1 L 2.1133 pt 1 g 0.0353 oz
1 ft 30.48 cm 1 qt 0.9464 L 1 lb 453.6 kg 1 cm 0.03281 ft 1 L 1.0567 qt 1 g 0.002205 lb
1 yd 0.9144 m 1 gal 3.785 L 1 lb 0.4536 kg 1 m 1.0936 yd 1 L 0.2642 gal 1 kg 2.205 lb
1 mi 1.609 km 1 km 0.6215 mi