8.6 Conic Sections Types Standard Equation Forms

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Presentation transcript:

8.6 Conic Sections 1 2 3 Types Standard Equation Forms Practice Problems

Types of Conic Sections Parabolas

Types of Conic Sections Circles

Types of Conic Sections Elipses

Types of Conic Sections Hyperbolas

Standard Equation Form Conic Section Standard Equation Form Parabola Circle

Standard Equation Form Conic Section Standard Equation Form Hyperbola

Standard Equation Form Conic Section Standard Equation Form Elipse

Identifying a Conic Section by Rewriting into Standard Form Isolate the terms Variables on the left of the equal sign Constants on the right of the equal sign Complete the square Factor Compare to the Standard Forms

Identifying a Conic Section by Rewriting into Standard Form Example Write the equation in standard form and identify the type of conic section it is.

Identifying Conic Sections by Analyzing Coefficients Put the equation into the form Compare A and C using the following: Conic Section Relationship of A to C Parabola A=0 or C=0, not both Circle A=C Ellipse A & C have the same sign and are not equal Hyperbola A & C have opposite signs

Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A and C have opposite signs, it is a hyperbola

Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A = C , it is a circle

Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A and C are both positive and not equal, it is a parabola

Practice Problems Page 450 Problems 4-9, 12-29, 33-38