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Classifying Conics 10.6. What is the general 2 nd degree equation for any conic? What information can the discriminant tell you about a conic?. The equation of any conic can be written in the form-. Called a general 2 nd degree equation. Circles. Can be multiplied out to look like this….

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classifying conics 10 6
Classifying Conics10.6

What is the general 2nd degree equation for any conic?

What information can the discriminant tell you about a conic?

the equation of any conic can be written in the form

The equation of any conic can be written in the form-

Called a general 2nd degree equation

circles
Circles

Can be multiplied out to look like this….

ellipse
Ellipse

Can be written like this…..

parabola
Parabola

Can be written like this…..

hyperbola
Hyperbola

Can be written like this…..

how do you know which conic it is when it s been multiplied out
How do you know which conic it is when it’s been multiplied out?
  • Pay close attention to whose squared and whose not…
  • Look at the coefficients in front of the squared terms and their signs.
circle
Circle

Both x and y are squared

And their coefficients are the same number and sign

ellipse1
Ellipse
  • Both x and y are squared
  • Their coefficients are different but their signs remain the same.
parabola1
Parabola
  • Either x or y is squared but not both
hyperbola1
Hyperbola
  • Both x and y are squared
  • Their coefficients are different and so are their signs.
you try
You Try!
  • Ellipse
  • Parabola
  • Hyperbola
  • Circle
  • Hyperbola
  • Parabola
  • Circle
  • Ellipse
  • Hyperbola
  • Ellipse
when you want to be sure
When you want to be sure…

of a conic equation, then find the type of conic using discriminate information:

Ax2 +Bxy +Cy2 +Dx +Ey +F = 0

B2 − 4AC < 0, B = 0 & A = C Circle

B2 − 4AC < 0 & either B≠0 or A≠C Ellipse

B2 − 4AC = 0 Parabola

B2 − 4AC > 0 Hyperbola

classify the conic
Classify the Conic

2x2 + y2−4x − 4 = 0

Ax2 +Bxy +Cy2 +Dx +Ey +F = 0

A = 2

B = 0

C = 1

B2 − 4AC = 02 − 4(2)(1) = −8

B2 − 4AC < 0, the conic is an ellipse

graph the conic
Graph the Conic

2x2 + y2−4x − 4 = 0

2x2−4x + y2 = 4

2(x2−2x +___)+ y2 = 4 + ___ (−2/2)2= 1

2(x2−2x +1)+ y2 = 4 + 2(1)

2(x−1)2 + y2 = 6

V(1±√6), CV(1±√3)

Complete the Square

steps to complete the square
Steps to Complete the Square

1. Group x’s and y’s. (Boys with the boys and girls with the girls) Send constant numbers to the other side of the equal sign.

2. The coefficient of the x2 and y2 must be 1. If not, factor out.

3. Take the number before the x, divide by 2 and square. Do the same with the number before y.

4. Add these numbers to both sides of the equation. *(Multiply it by the common factor in #2)

5. Factor

slide18
What is the general 2nd degree equation for any conic?

What information can the discriminant tell you about a conic?

B2- 4AC < 0, B = 0, A = C Circle

B2- 4AC < 0, B ≠ 0, A ≠ C Ellipse

B2- 4AC = 0, Parabola

B2- 4AC > 0 Hyperbola

assignment 10 6
Assignment 10.6

Page 628, 29-55 odd

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