red pen highlighter notebook calculator ruler Graph the

red pen, highlighter, notebook, calculator, ruler Graph the hyperbola. Identify the vertices, foci, and equations of the asymptotes. +2 box and asymptotes +2 hyperbola – 1) careful c 2 =when a 2 + you b 2 Center: (2, Be write the c 2 center. = 25 + 49 a = 5 +1 +1 Look VERY carefully 2 c = 74 +1 b = 7 +1 at the equation. c = 8. 60 +1 c ≈ 8. 60 foci: (2, – 1± 8. 60) – 10 10 total: y +1 +1 10 +1 +1 (2, – 9. 60) and (2, 7. 60) +2 +1 vertices: (2, – 6) and (2, 4) +2 asymptotes: +2 x – 10 +1

Characteristics of Conic Sections From this point on, you will write and graph conic sections equations without being told the type of equation you are working with. Here are some characteristics to help you distinguish between types of conics based on the equations: Only y and x 2… or… only x and y 2 Parabola: ______________________ x 2 and y 2, and they have the same, positive coefficients Circle: ________________________ x 2 and y 2, and they have different, but positive coefficients Ellipse: _______________________ x 2 and y 2, and they have different signs (+/–) Hyperbola: ______________________ Helpful hint: Whenever you are going to classify conic equations, be sure to have all the variables (especially x 2 and y 2) on the same side of the equation.

I. Without writing the equation in standard form, state whether the graph of each equation is a parabola, circle, ellipse, or hyperbola. 1) circle 2) parabola 4) 3) hyperbola ellipse 6) 5) hyperbola circle 8) 7) ellipse 10) 9) parabola hyperbola 12) 11) ellipse circle

II. Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. 1) parabola +4 – 4

II. Write each equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. 2) 9 hyperbola + 2 x + 1 36 36 – 4 y + 4 36 9 – 16

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