Classifying conics 10 6
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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

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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 = CCircle

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

B2 − 4AC = 0Parabola

B2 − 4AC > 0Hyperbola


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


Write the equation in standard form by completing the square

Write the equation in standard form by completing the square


Classifying conics 10 6

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 = CCircle

B2- 4AC < 0, B ≠ 0, A ≠ CEllipse

B2- 4AC = 0,Parabola

B2- 4AC > 0Hyperbola


Assignment 10 6

Assignment 10.6

Page 628, 29-55 odd


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