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Difference Foci Center Vertex Asymptotes Transverse Axis Conjugate Axis

HYPERBOLAS. Difference Foci Center Vertex Asymptotes Transverse Axis Conjugate Axis. y. b. c. transverse axis. x. a. conjugate axis. F. F. 1. 2. Standard 4, 9,16, 17. PARTS OF A HYPERBOLA. asymptote. asymptote. vertex. vertex. y. -. 2. 2. 2. c = a + b. x. y.

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Difference Foci Center Vertex Asymptotes Transverse Axis Conjugate Axis

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  1. HYPERBOLAS Difference Foci Center Vertex Asymptotes Transverse Axis Conjugate Axis

  2. y b c transverse axis x a conjugate axis F F 1 2 Standard 4, 9,16, 17 PARTS OF A HYPERBOLA asymptote asymptote vertex vertex

  3. y - 2 2 2 c = a + b x y 2 2 (x – h) (y – k) = 1 2 2 (y – k) (x – h) = 1 x - 2 2 a b 2 2 a b For both equations. F F F F 1 2 2 1 Standard 4, 9, 16, 17 STANDARD EQUATIONS OF A HYPERBOLA • Hyperbola with center at (h,k) with horizontal axis • has equation In this case, transverse axis is horizontal. • Hyperbola with center at (h,k) with vertical axis has equation In this case, transverse axis is vertical. NOTE: These two hyperbolas are graphed with center (0,0)

  4. y 10 2 2 2 8 c = a + b 6 4 2 -10 x -8 -6 -4 -2 2 8 6 10 4 -2 -4 -6 -8 2 c = 25 + 9 5.8 c= 34 2 2 (x -(+3)) (y-(+4)) - =1 9 25 2 2 c = 34 b = 9 2 a = 25 2 2 (x-3) (y-4) - =1 9 25 Standard 4, 9, 16, 17 Draw the hyperbola that is represented by: h= 3 Center = (3,4) k= 4 a = 5 b= 3 Focus 1= (h+c, k) = (3+5.8,4) = (8.8,4) = (3-5.8,4) Focus 2= (h-c, k) = (-2.8,4)

  5. y 20 16 2 2 2 c = a + b 12 8 4 -20 x -16 -12 -8 -4 16 12 20 8 4 -4 -8 -12 -16 2 c = 81 + 64 12 c= 145 2 2 (y-(+6)) (x-(-2)) - =1 64 81 2 2 c = 145 b = 64 2 a = 81 2 2 (y-6) (x+2) - =1 64 81 Standard 4, 9, 16, 17 Draw the hyperbola that is represented by: h= -2 Center = (-2,6) k= 6 a = 9 b= 8 Focus 1= (h+c, k) = (-2,6+12) = (-2,18) = (-2,6-12) Focus 2= (h-c, k) = (-2,-6)

  6. y 10 2 2 2 8 c = a + b 13 13 13 13 13 13 2 2 6 -a -a 4 2 2 2 b = c - a 2 (-1,0) -10 x -8 -6 -4 -2 2 8 6 10 4 (2,0) -2 -4 -6 -8 (5,0) 2 2 2 2 -9 b = (x – h) (y – k) (2- , 0) (2+ , 0) (2+ , 0) = 1 If = 2 b = 13-9 2 2 (x-(+2)) (y-(0)) 2 2 2+c 2+c - - =1 2 a 4 9 2 b = 4 2 b 2 a = 9 2 2 (x-2) y - =1 2 + c = 2 + c = 4 9 Standard 4, 9, 16, 17 Given the graph below obtain the equation of the hyperbola. Transverse axis is 6 units: 2a=6 a = 3 Focus2 Focus1 then we know: From the figure: h= 2 Center = (2,0) k= 0 Hyperbola is horizontal: Focus1 =( h+c,k) then -2 -2

  7. y 10 2 2 2 8 c = a + b 13 13 13 13 13 13 2 2 6 -a -a 4 2 2 2 b = c - a 2 -10 x -8 -6 -4 -2 2 8 6 10 4 -2 -4 (4,-2) -6 -8 2 2 2 2 -4 b = (y – k) (x – h) = 1 If 2 b = 13-4 (4,-2- ) (4,-2+ ) 2 2 (y-(-2)) (y-(4)) 2 2 -2+c -2+c - - =1 2 a 9 4 2 b = 9 = (4,-2+ ) 2 b 2 a = 4 2 2 (y+2) (x-4) - =1 -2 + c = -2 + c = 9 4 Standard 4, 9,16, 17 Given the graph below obtain the equation of the hyperbola. Transverse axis is 4 units: Focus1 2a=4 a = 2 then we know: Focus2 From the figure: h= 4 Center = (4,-2) k= -2 Focus1 =( h,k+c) Hyperbola is vertical: then +2 +2

  8. 2 Ax + Bxy + Cy + Dx + Ex + F = 0 2 Standard 4, 9, 16, 17 Equation of a Conic Section

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