## Optional Conics Unit

Conics are quadratic relations that not necessarily functions.  They used to be in the Grade 11U curriculum, but are no longer required.  If you would like, you can learn it for yourself.  It is not hard to do, but it will take some time.  The level of difficulty is just more algebra with quadratics, and graphic some new curves (some you already know!).

The conics:

• Circle (we know these)
• Parabola (we know the function form,  but the other, )
• Ellipse  (new!)
• Hyperbola  (new!)

It’s in your textbook.  This outline goes back to when I used to assign this in class. This gives you an idea of how much work is involved.  Since you are learning it for yourself, you can go through the work faster by skipping practice questions and using a formula sheet (or cheat sheet, if you like).  There’s no test, so it doesn’t matter.  It is standard material in the US, so if you are planning to do SATs to apply to university in the US, this will help.

# Work

0

Textbook homework:

§8.2 Equations of Loci

In-class:

§8.1 constructing loci using GSP P588—593  #1—47

P598 #1—3, 6, 7, 11

(Skip this.)

0

§8.3 Technology: Loci and Conics

• Ellipse P601 #1—17
• 21Hyperbola P603 #18 – 34
• Parabolas P606 #35—49

Handout, Conic Locus  (Draw all 4 conics, point by point using the locus definitions.)

(This day of homework is easy to skip.  The exercises are to build the conic relations using Geometer Sketchpad.)

0

§8.4 The Circle

P614 #5b, 6, 10a, 14, 17, 21, 24, 26, 27, 29

(This day of homework is easy to skip assuming you are proficient with the equation of a circle.)

1

§8.5 The Ellipse

P632 #1—5, 7—9, 20

2

§8.6 Hyperbolas

P648 #1, 2; 3—6 (odd), 10, 16

3

§8.7 Parabolas

Create a summary of all conics.

P661 #1—5 (odd); 6, 8, 12, 14

(DON’T skip this.  It’s very different working with the definition of a directrix and focus.)

4

§8.8 Conics in expanded form

Summarize

• Working with the expanded form,

P672 #1—4, 6

5

§8.9 Intersections of Lines and Conics

Conic Systems

Enrichment:  Solving algebraically for points of intersection given two conics (quadratic systems)

• Identify the types of conics in each example
• Practise solving one of each case

optional P684 #1ace, 2ace

P684 #3ace, 4(do NOT round-off), 11, 15

6

Work Period

Practice Set – Conics

P689—693 Review Conics