math trig worksheet

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Math 1083 Worksheet 20 Getting Ready for Ellipses

Objectives: 1. Review distance formula

2. Review completing the squares

3. Review the equation for a circle

Review: Given two points 𝐴 (𝑥1, 𝑦1) 𝑎𝑛𝑑 𝐵(𝑥2, 𝑦2)

➢ The distance between A and B is: 𝒅 = √(𝒙𝟐 − 𝒙𝟏) 𝟐 + (𝒚𝟐 − 𝒚𝟏)

𝟐

➢ The midpoint is ( 𝑥1+𝑥2

2 ,

𝑦1+𝑦2

2 )

#1 Find the distance and midpoint between each pair of points. Give the exact answer.

a) (−2, 3), (−3, −3) b) (2, −3), (−1, 4)

#2 Find the coordinates of A and the distance AB, AC and BC

a)

b)

49

#3 Find the value of 𝑐 that completes the square. a) 𝑟2 − 6𝑟 + 𝑐 = ( )2 b) 𝑝2 + 12𝑝 + 𝑐 = ( )2

c) 𝑥2 − 3𝑥 + 𝑐 = ( )2 d) 𝑦2 − 𝑦 + 𝑐 = ( )2 #4 A student tried to complete the squares for 𝑥2 + 4𝑥 = 4, but something was wrong in her computation. Identify the error in her procedure and make correction.

First, find the missing constant: since 𝑏

2 =

4

2 = 2, get (

𝑏

2 )

2

= 22 = 4

Next, add 4 to the equation: 𝑥2 + 4𝑥 + 4 = 4 Lastly, factor the trinomial: (𝑥 + 2)2 = 22 REVIEW: The equation of a circle centered at (ℎ, 𝑘) and with radius R is

(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑅2

#5 Identify the center and radius of each. Then sketch the graph. a) (𝑥 − 1)2 + (𝑦 + 3)2 = 4 b) 𝑥2 + 2𝑥 + 𝑦2 = 15