red pen highlighter GP notebook calculator ruler Graph

red pen, highlighter, GP notebook, calculator, ruler Graph the hyperbola. Identify the vertices, foci, and asymptotes. 10 +1 +1 c 2 = a 2 + b 2 c 2 = 9 + 36 c 2 = 45 +2 hyperbola y +1 +1 (0, 3) Center: (0, 0) a = 3 +1 (6, 0) x (– 6, 0) b = 6 +1 10 c ≈ 6. 71 – 10 +1 +1 c = 6. 71 +1 foci: (0, ± 6. 71) +2 (0, – 3) vertices: (0, ± 3) +2 +1 +2 box & asymptotes +1 asymptotes: – 10 total: +2

Conic Sections: Hyperbolas with Center (h, k) Standard Form of Equation Graph (sketch) Direction of Transverse Axis Center horizontal (h, k) vertical (h, k) Foci (h±c, k) (h, k±c) Vertices (h±a, k) (h, k±a) Length of Transverse Axis Length of Conjugate Axis Equations of Asymptotes 2 a 2 a 2 b 2 b

I. Graph each hyperbola. Label the vertices and foci. Determine the equations of the asymptotes. Which variable is positive? x So, it’s a horizontal hyperbola a) 10 Center: (– 1, – 3) a= 2 b= 3 c = 3. 61 foci: (– 1± 3. 61, – 3) c 2 = a 2 + b 2 c 2 = 4 + 9 c 2 = 13 c ≈ 3. 61 – 10 (– 4. 61, – 3) and (2. 61, – 3) 10 (– 3, – 3) (1, – 3) vertices: (– 3, – 3) and (1, – 3) asymptotes: y – 10 x

I. Graph each hyperbola. Label the vertices and foci. Determine the equations of the asymptotes. b) Which variable is positive? y So, it’s a vertical hyperbola 10 Be you 4) carefulc 2 when Center: (– 2, = a 2 + b 2 write the center. 2 = 16 + 9 a= 4 c Look VERY carefully b= 3 c 2 = 25 at the equation. c= 5 foci: (– 2, 4± 5) – 10 c=5 (– 2, 8) (– 2, 0) 10 (– 2, – 1) and (– 2, 9) vertices: (– 2, 0) and (– 2, 8) asymptotes: y – 10 x

Take a few minutes to complete Part I.

II. Write the standard form equation for each hyperbola. a) 2 y The hyperbola opens left and right. Therefore, x is positive. – 2 12 “a” will be under x. center: (5, – 5) a= 3 b= 2 c= equation: (x – 5)2 32 (y + 5)2 22 a b – 12 x

II. Write the standard form equation for each hyperbola. d) The hyperbola opens up and down. 10 y Therefore, y is positive. “a” will be under y. center: (6, 3) a= 4 b= 3 c= 5 equation: (y – 3)2 42 a c x – 1 – 4 (x – 6)2 32 13

Take a few minutes to complete Part II.

III. Write the standard form equation for each hyperbola. a) Group the x’s and y’s together just like we do for circles and ellipses. Notice the y’s. Recall that subtracting is the same thing as adding a negative. Complete the square. To complete the square for the y’s, first factor out – 4. What number is really “added” by the y’s? ? ? 9 4 – 4 y + 4 – 4 4 4 9 – 16 Hyperbolas must equal 1, so divide everything by 4.

III. Write the standard form equation for each hyperbola. d) Group the x’s and y’s together just like we do for circles and ellipses. Notice the y’s are first since y 2 is positive. Note how the x’s are “added. ” Complete the square. To complete the square for the x’s, first factor out – 3. What number are we really adding to each side? 8 – 4 y + 4 24 24 + 4 x + 4 – 3 24 32 – 12 Hyperbolas must equal 1, so divide everything by 24.

Complete today’s packet.