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# Warm Up - PowerPoint PPT Presentation

Warm Up. What is the standard form of a parabola? What is the standard form of a circle? What is the standard form of a ellipse? What is the standard form of a hyperbola?. Algebra 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 6: Graphing and Classifying Conics. VOCAB.

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Presentation Transcript

• What is the standard form of a parabola?

• What is the standard form of a circle?

• What is the standard form of a ellipse?

• What is the standard form of a hyperbola?

### Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

• Conics or Conic Sections – parabolas, circles, ellipses, and hyperbolas…basically all curves that are formed by the intersections of a plane and a double-napped cone

• Discriminant – an equation that can tell what type of conic you have

• Today we are going to learn one way to classify a conic section. This way is to put it in a normal formula.

• Parabola

• or

• Circle

• Ellipse

• or

• Hyperbola

• or

• Look at the powers of x and y

• If ONLY one of them is squared…parabola

• Get x and y on the same side

• Divide by the number

• If it is SUBTRACTION…Hyperbola

• Denominators are the same…Circle

• Denominators are different…Ellipse

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• What did you learn today?

• NONE

• Name the 4 types of conic sections

• Explain how to classify a conic section

### Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

• Today we are going to learn one way to classify a conic section. This way is to find the discriminant

• General Equation

• Discriminant

• Discriminant

• Less than zero

• B = 0 and A = C …it’s a circle

• B ≠ 0 or A ≠ C … it’s an ellipse

• Equal zero

• It’s a parabola

• Greater than zero

• It’s a hyperbola

• Find a, b, c

• Find the discriminant

• Classify the conic

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• Classify the conic section

• 1.

• 2.

• 3.

• 4.

• What did you learn today?

• Worksheet

• 10.6B (9 – 14)

• Classify the conic

• 1.

• 2.

### Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

• Today we are going to learn how to write equations of conics that are NOT in the center of a graph

• Parabola

• or

• Circle

• Ellipse

• or

• Hyperbola

• or

• Center of all shapes is

• (h , k)

• A is the distance from the vertex to the center

• C is the distance from the focus to the center

• Label what you know

• A, b, c, p, h, k

• Plug into the

• Write the equation of the conic section

• 1. Parabola … V (-2, 1) F (-3, 1)

• 2. Circle … Center (3, -2) r = 4

• 3. Ellipse … F (3, 5) (3, -1) V (3, 6) (3, -2)

• 4. Hyperbola … V (5, -4) (5, 4) F (5, -6) (5, 6)

• Write the equation of the conic section

• 1. Parabola … V (1, -2) F (1, 1)

• 2. Circle … Center (9, 3) r = 4

• 3. Ellipse … V(2, -3) (2, 6) F (2, 0) (2, 3)

• 4. Hyperbola … V (-4, 2) (1, 2) F (-7, 2) (4, 2)

• Write the equation of the conic section

• 1. Parabola … V (-3, 1) directrix x = -8

• 2. Circle … Center (-4, 2) r = 3

• 3. Ellipse … F (-2, 2) (4, 2) CV (1, 1 (1, 3)

• 4. Hyperbola … V (8, -4) (8, 4) F (8, -6) (8, 6)

• Today you learned how to write the equation of a translated conic

• Worksheet

• 10.6B (1 – 4)